#geometry-and-trigonometry | Mathematics | Page 221

tacit meteor Jul 29, 2019, 1:33 PM

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just simple trig

idle bloom Jul 29, 2019, 1:36 PM

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This looks kinda arbitrary

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Like is there some sort of set of rules?

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Like the lines and corners you high lighted just now, why those and why not other ones

tacit meteor Jul 29, 2019, 1:37 PM

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they cross the hypotnese

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we start out with 4 poitns

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2 points for each line

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which we have the coordinates for

idle bloom Jul 29, 2019, 1:38 PM

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Why not the line I just highlighted in red

tacit meteor Jul 29, 2019, 1:39 PM

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that line was just the other side of the rectangle

idle bloom Jul 29, 2019, 1:39 PM

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Hmmm ok

tacit meteor Jul 29, 2019, 1:40 PM

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we use those points because they are horizantal and vertical to the hypoteneus

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i wrote a program that does it and it works

idle bloom Jul 29, 2019, 1:40 PM

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I'm not sure how to extend this to planes though

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Oh neat

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That would have been probably better to show but I have no programming experience

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It's a cool idea tho

tacit meteor Jul 29, 2019, 1:40 PM

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if both slope are positive it is slighty different but same concept

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yeah it totatly works im quite happy as i figured it out on my own

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if i can extend it to line plane intersesction i can write my own raytracer

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thanks anyways

worthy root Jul 29, 2019, 3:31 PM

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📎 JPEG_20190729_210103.jpg

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Can anyone explain me this ?

dark sparrow Jul 29, 2019, 3:35 PM

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what is giving you trouble here?

worthy root Jul 29, 2019, 3:36 PM

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I found the x and y intercepts

dark sparrow Jul 29, 2019, 3:36 PM

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ok

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what are they

worthy root Jul 29, 2019, 3:36 PM

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x=-2,3

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y=18

dark sparrow Jul 29, 2019, 3:36 PM

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so your points are (-2, 0), (3,0) and (0,18)

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those are the three vertices of your triangle

worthy root Jul 29, 2019, 3:37 PM

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Oh

dark sparrow Jul 29, 2019, 3:37 PM

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if you draw it, it'll be obvious how to find its area

worthy root Jul 29, 2019, 3:37 PM

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Ok donr

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Done*

tacit meteor Jul 29, 2019, 4:14 PM

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do 2 triangles with equal sides have the same angles?

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do 2 triangels which each have 3 sides that are equal have the same angles?

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another way to ask the question is, how many unique trianlges that have the same length of sides can you build

olive solar Jul 29, 2019, 4:16 PM

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oh wait are you asking or trying to explain

tacit meteor Jul 29, 2019, 4:16 PM

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im asking

olive solar Jul 29, 2019, 4:17 PM

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first one: no;
second one: yes

tacit meteor Jul 29, 2019, 4:17 PM

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its the same quession

olive solar Jul 29, 2019, 4:17 PM

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wait. shit. i misread the first one lol

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if two triangles all have sides of the same length between them, then they are considered equivalent

tacit meteor Jul 29, 2019, 4:19 PM

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they are the same triangle?

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so that mean they have equal angles?

olive solar Jul 29, 2019, 4:19 PM

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they have equal angles, yes

tacit meteor Jul 29, 2019, 4:19 PM

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ok thanks

olive solar Jul 29, 2019, 4:19 PM

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they are equivalent triangles

tacit meteor Jul 29, 2019, 4:19 PM

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is this proven

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?

worthy root Jul 29, 2019, 5:28 PM

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Yes it is

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Also you can just experimentally verify this thing

tacit meteor Jul 29, 2019, 6:04 PM

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then how come i cant extract an angle from a point using 3 coordinates of 3 points

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using coordinates of 3 points

fringe dirge Jul 29, 2019, 6:26 PM

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You can

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This is what the law of cosines does

fossil ledge Jul 29, 2019, 7:22 PM

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You can’t, but I can KEK

tacit meteor Jul 29, 2019, 7:56 PM

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ok ill try on my own

quiet mason Jul 29, 2019, 8:03 PM

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hey orange popsicle you can derive it on your own you know

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just draw a triangle and a perpendicular to one of the bases and work it out

tacit meteor Jul 29, 2019, 8:11 PM

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you can with right triangles but not just rrandom triangle

fringe dirge Jul 29, 2019, 9:17 PM

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You can do it with any triangle

upper karma Jul 29, 2019, 11:08 PM

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If I scale down a figure 5 times less in size what is the scale factor

dire rampart Jul 29, 2019, 11:09 PM

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1/5

spark stag Jul 29, 2019, 11:12 PM

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wdym

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"5 times less in size"

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if its the length 5 times less

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the scale factor is 1/5

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if its the area

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then the scale factor of length is 1/25

upper karma Jul 29, 2019, 11:29 PM

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okay thanks

echo trench Jul 30, 2019, 1:51 AM

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📎 image0.jpg

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Any help on this?

queen python Jul 30, 2019, 1:52 AM

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@echo trench

echo trench Jul 30, 2019, 1:52 AM

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@queen python Yes hello

fossil ledge Jul 30, 2019, 1:52 AM

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other two angles not confirmed to be 60

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unless im missing something

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yea no they arent

queen python Jul 30, 2019, 1:53 AM

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Let me explain

fossil ledge Jul 30, 2019, 1:53 AM

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go for it Bongo, I believe in you

queen python Jul 30, 2019, 1:53 AM

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What do all the sides of a polygon have to add up too

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360 degrees

echo trench Jul 30, 2019, 1:53 AM

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I know I was just conflicting with it as I thought it created a whole new triangle which had to equal 180 degrees.

fossil ledge Jul 30, 2019, 1:53 AM

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uhhhhh

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Bongo

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triangles add to 180

queen python Jul 30, 2019, 1:54 AM

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Yeah

fossil ledge Jul 30, 2019, 1:54 AM

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pentagons add to 540

queen python Jul 30, 2019, 1:54 AM

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Ik

fossil ledge Jul 30, 2019, 1:54 AM

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What do all the sides of a polygon have to add up too
360 degrees

queen python Jul 30, 2019, 1:54 AM

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im aware

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fine

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I'll be smart about it

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In the shape below your 60-60-60 triangle

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All the sides must add up to 360

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You see how there are the squares that mean 90 degrees

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We can see that we already have 60 degrees

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so the other side must be 30

echo trench Jul 30, 2019, 1:56 AM

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Ohhhhh, ok ok.

fossil ledge Jul 30, 2019, 1:56 AM

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wait but the triangle isnt 60-60-60

queen python Jul 30, 2019, 1:57 AM

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He wrote 60-60-60

echo trench Jul 30, 2019, 1:57 AM

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@fossil ledge It is not?

fossil ledge Jul 30, 2019, 1:57 AM

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no

echo trench Jul 30, 2019, 1:57 AM

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Oh waiiit

queen python Jul 30, 2019, 1:57 AM

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So I assume he was right

fossil ledge Jul 30, 2019, 1:57 AM

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lets look at the angle with theta

queen python Jul 30, 2019, 1:57 AM

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that's 16

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90-16

echo trench Jul 30, 2019, 1:57 AM

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Is it because the 60 degree is with the bigger triangle

fossil ledge Jul 30, 2019, 1:57 AM

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the other side is 90 degrees and we subtract at 16

queen python Jul 30, 2019, 1:57 AM

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That's the other angle

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84

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76

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74

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I can't do basic math

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Fml

fossil ledge Jul 30, 2019, 1:58 AM

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74

queen python Jul 30, 2019, 1:58 AM

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So we now that that side

fossil ledge Jul 30, 2019, 1:58 AM

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so now 180-60-74 will give you the other angle of your top triangle

queen python Jul 30, 2019, 1:58 AM

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Now what about the other side

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^

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i was bout to say that

fossil ledge Jul 30, 2019, 1:58 AM

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that angle + phi (what you are solving for) should add up to 90

queen python Jul 30, 2019, 1:59 AM

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so the angle you need is

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180-60-74 90-answer

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you comprehend

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?

echo trench Jul 30, 2019, 2:00 AM

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No, I really don't understand

queen python Jul 30, 2019, 2:01 AM

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Ok

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so a triangles sides add up to 180

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Right

echo trench Jul 30, 2019, 2:01 AM

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Yes

queen python Jul 30, 2019, 2:01 AM

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we know that theta is 16

echo trench Jul 30, 2019, 2:01 AM

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Ok thats called theta

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Alright

queen python Jul 30, 2019, 2:01 AM

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do you mind re sending the photo

echo trench Jul 30, 2019, 2:02 AM

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Yuppp

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https://cdn.discordapp.com/attachments/326138757474680852/605578268007071744/image0.jpg

queen python Jul 30, 2019, 2:02 AM

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we can see that the angle above theta + theta =90

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Because if the square

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So we have 16+x=90

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We subtract 16 from both sides

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And get x=74

echo trench Jul 30, 2019, 2:03 AM

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Question

queen python Jul 30, 2019, 2:03 AM

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?

echo trench Jul 30, 2019, 2:03 AM

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Where did you get the other theta, to make the equation theta + theta= 90

fossil ledge Jul 30, 2019, 2:04 AM

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angle above theta*

queen python Jul 30, 2019, 2:04 AM

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^

echo trench Jul 30, 2019, 2:04 AM

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The 90 degrees>

queen python Jul 30, 2019, 2:04 AM

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angle above theta + theta =90

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the aren't greater than

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They are 90

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because we see the square that means they make a right angle

echo trench Jul 30, 2019, 2:05 AM

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Oh sorry, the greater than was a typo

queen python Jul 30, 2019, 2:05 AM

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Oh

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ok now we know we have 60 +74

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What is that?

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134

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so now we do 180-134

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Do you know why?

echo trench Jul 30, 2019, 2:06 AM

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First off

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We subtracted 90 and 16 to get 74,

queen python Jul 30, 2019, 2:07 AM

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yes

echo trench Jul 30, 2019, 2:07 AM

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Which is 74 degrees to the other side of the 16 right?

queen python Jul 30, 2019, 2:07 AM

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Yes

echo trench Jul 30, 2019, 2:07 AM

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And we subtracted it bc?

queen python Jul 30, 2019, 2:08 AM

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we know that the side opposite of theta + 16=90

echo trench Jul 30, 2019, 2:08 AM

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Ahhhhhh

queen python Jul 30, 2019, 2:08 AM

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so we solved for that side

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x+16=90

echo trench Jul 30, 2019, 2:08 AM

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And then from there

queen python Jul 30, 2019, 2:08 AM

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Subtract 16 from both side

echo trench Jul 30, 2019, 2:08 AM

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cool cool

queen python Jul 30, 2019, 2:08 AM

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why did we add 60?

echo trench Jul 30, 2019, 2:08 AM

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Now we use that 74 and add it with the 60

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To find the missing side, which is opposite of phi

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74+60=134

queen python Jul 30, 2019, 2:09 AM

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Yes

echo trench Jul 30, 2019, 2:09 AM

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x+134=180

queen python Jul 30, 2019, 2:09 AM

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yes

echo trench Jul 30, 2019, 2:09 AM

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-134 on both sides

queen python Jul 30, 2019, 2:09 AM

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good

echo trench Jul 30, 2019, 2:10 AM

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180-134=46

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That angle is 46 degrees

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But we still have to find phi

queen python Jul 30, 2019, 2:10 AM

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now what is it?

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Use thes ame concept we used to find 74

echo trench Jul 30, 2019, 2:10 AM

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and with the knowledge that i learned with theta and the 90 degrees

queen python Jul 30, 2019, 2:10 AM

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*same concept

echo trench Jul 30, 2019, 2:11 AM

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I basically would work backwards, so

queen python Jul 30, 2019, 2:11 AM

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in this case it is 90 degrees

echo trench Jul 30, 2019, 2:11 AM

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90-46=

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which is 44

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so phi-44?

queen python Jul 30, 2019, 2:11 AM

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in other cases it can be diffrent degrees

echo trench Jul 30, 2019, 2:11 AM

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*=

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okkk

queen python Jul 30, 2019, 2:11 AM

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yes

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good

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The answer is 44

echo trench Jul 30, 2019, 2:11 AM

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wow...

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I actually did geometry

queen python Jul 30, 2019, 2:11 AM

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You did it 😃

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good

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i just learned geometry last week

echo trench Jul 30, 2019, 2:12 AM

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Thank you so much actually Bongo

fossil ledge Jul 30, 2019, 2:12 AM

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good job both of you pandaHugg

echo trench Jul 30, 2019, 2:12 AM

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You too Goat

queen python Jul 30, 2019, 2:12 AM

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Now I act like I'm a master

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thanks

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If you need anymore help feel free to ask

fossil ledge Jul 30, 2019, 2:12 AM

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teaching is a great tool to make sure you understand the material

echo trench Jul 30, 2019, 2:12 AM

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I struggle in math, my home country was never full on that

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lol

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Thank you guys

queen python Jul 30, 2019, 2:12 AM

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o

fossil ledge Jul 30, 2019, 2:12 AM

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pretty much why im here, just to practice my foundations

echo trench Jul 30, 2019, 2:13 AM

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:-), thats so great

queen python Jul 30, 2019, 2:13 AM

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Im here cause I just am

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Woog invited me I think

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I joined long long ago

echo trench Jul 30, 2019, 2:13 AM

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I came around this week

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But this is my first time communicating

queen python Jul 30, 2019, 2:14 AM

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well hopefully we se you around here

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And you can help someone some day

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do you have any other questions?

echo trench Jul 30, 2019, 2:16 AM

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Nope but if you need help, I'll try my best. I'm more with english, and history so ask me there lol

queen python Jul 30, 2019, 2:19 AM

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O

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If it's us history I can help

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or world or euro

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English depends

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if you want help analyzing anything I can help

echo trench Jul 30, 2019, 2:20 AM

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@queen python Are you in the AP discord server?

queen python Jul 30, 2019, 2:20 AM

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What's that?

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Send me the link

echo trench Jul 30, 2019, 2:21 AM

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Wait do you take AP bongo?

queen python Jul 30, 2019, 2:21 AM

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I am gonna

trail minnow Jul 30, 2019, 2:21 AM

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bongo is not in hs yet

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lmao

echo trench Jul 30, 2019, 2:21 AM

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Oppp

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Bongo you hecka smart

trail minnow Jul 30, 2019, 2:21 AM

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what Aps are you taking?

echo trench Jul 30, 2019, 2:21 AM

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Physics and World

trail minnow Jul 30, 2019, 2:21 AM

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ah

queen python Jul 30, 2019, 2:21 AM

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Woah

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Im taking world and comp sci freshmen

trail minnow Jul 30, 2019, 2:22 AM

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im taking world, euro, chem, and comp sci this year as a soph tinktonk

queen python Jul 30, 2019, 2:22 AM

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physics and something else next year

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sophomore im not sure yet

trail minnow Jul 30, 2019, 2:22 AM

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well i took ap world class as a freshman but it's a 2 year class

echo trench Jul 30, 2019, 2:22 AM

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Where do you guys school at?

trail minnow Jul 30, 2019, 2:22 AM

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nyc

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mniip

queen python Jul 30, 2019, 2:22 AM

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Nyc

echo trench Jul 30, 2019, 2:22 AM

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Earth Quake state 😃

trail minnow Jul 30, 2019, 2:22 AM

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ah

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i go to [REDACTED]

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bongo if u dox me i s2g

echo trench Jul 30, 2019, 2:23 AM

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California is kinda harsh on AP and its kinda sad

queen python Jul 30, 2019, 2:23 AM

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i wont exspose u

trail minnow Jul 30, 2019, 2:23 AM

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mniip

queen python Jul 30, 2019, 2:23 AM

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expose

trail minnow Jul 30, 2019, 2:23 AM

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i've been considering adding macro on to the list

echo trench Jul 30, 2019, 2:23 AM

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Like specific AP courses are only for one grade and its pretty sad

queen python Jul 30, 2019, 2:23 AM

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we can take any ap

trail minnow Jul 30, 2019, 2:23 AM

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cause i was prepping for euro this summer and immediately got a 90% and realized that i actually did not need to do as much prep as i thought i would

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so i have more room now

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ye

queen python Jul 30, 2019, 2:23 AM

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As long as we but the test

trail minnow Jul 30, 2019, 2:23 AM

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yes

queen python Jul 30, 2019, 2:23 AM

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buy

trail minnow Jul 30, 2019, 2:23 AM

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we can take any AP test here

queen python Jul 30, 2019, 2:23 AM

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we don't need the class

trail minnow Jul 30, 2019, 2:23 AM

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and any class if you ask and they decide you deserve it

echo trench Jul 30, 2019, 2:24 AM

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Shold we move this too #discussion

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l;ol

trail minnow Jul 30, 2019, 2:24 AM

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probably

queen python Jul 30, 2019, 2:24 AM

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Sure

upper karma Jul 30, 2019, 2:29 AM

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For example 5.6 to 5.2 is a change of 7.14%

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What would be the scale factor if everything was reduced by 7.14%

spark stag Jul 30, 2019, 2:30 AM

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,calc 5.2/5.6

somber coyoteBOT Jul 30, 2019, 2:30 AM

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Result:

0.92857142857143

spark stag Jul 30, 2019, 2:30 AM

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that

upper karma Jul 30, 2019, 2:31 AM

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so aprox 0.93:1 ratio?

spark stag Jul 30, 2019, 2:31 AM

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of image:original, yes

upper karma Jul 30, 2019, 3:51 AM

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isnt the first one the original

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usually for ratios

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so am i wrong

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@spark stag

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wait

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if we have the original and then we have a new one which is 2 times smaller what would the ratio be

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It will be 2:1 right?

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Or 1:0.5?

spark stag Jul 30, 2019, 4:06 AM

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those are equivalent

upper karma Jul 30, 2019, 4:06 AM

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okay

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But ratios are original:new?

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if we have the original and then we have a new one which is 2 times smaller what would the ratio be

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But this will be 2:1 right

spark stag Jul 30, 2019, 4:07 AM

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the ratio of what

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of the original to the new?

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then yes, it's 2:1 (or equivalent)

upper karma Jul 30, 2019, 4:07 AM

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Okay thanks

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So it usually goes from original to new

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📎 image0.png

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Isn’t this wrong

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If it goes from original to new shouldn’t the fraction be b/a

spark stag Jul 30, 2019, 4:12 AM

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when we talk about scale factors

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we use image/original

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or image:original

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or whatever

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thats how a scale factor is calculated

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since the scale factor is the value such that:

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$\text{original} \cdot \text{scale factor} = \text{image}$ \ and therefore \ $\text{scale factor} = \frac{\text{image}}{\text{original}}$

somber coyoteBOT Jul 30, 2019, 4:13 AM

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Namington:

📎 105878844061286400.png

spark stag Jul 30, 2019, 4:13 AM

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but you can make a ratio be whatever you want

upper karma Jul 30, 2019, 4:13 AM

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so if I had an image and it reduced by size in 7% the radio will be 1:0.93

spark stag Jul 30, 2019, 4:14 AM

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not quite

upper karma Jul 30, 2019, 4:14 AM

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I don’t understand

spark stag Jul 30, 2019, 4:14 AM

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when we're talking about a ratio

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its always a ratio of something to something else

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so you have to clarify what you're talking about

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just saying "the ratio" is meaningless

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"the ratio of original to image", however, is 1:0.93 as you said

upper karma Jul 30, 2019, 4:15 AM

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What do you mean by original and image

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Like old and new?

spark stag Jul 30, 2019, 4:15 AM

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yes

upper karma Jul 30, 2019, 4:16 AM

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So if I had an old image and it was reduced by 7% in total size into a new image it will be 1:0.93?

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@spark stag

spark stag Jul 30, 2019, 4:17 AM

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the ratio of old to new is 1:0.93, yes

upper karma Jul 30, 2019, 4:18 AM

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But the scale factor is 0.93:1

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?

spark stag Jul 30, 2019, 4:20 AM

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the scale factor of "size" is 0.93, as that's what you would multiply the "size" of the original by to get the image

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for example, if the "size" of the old is 15 cm, then we'd multiply that by 0.93 to get the "size" of the new

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(note that i'm assuming we're talking about a spot where units line up, here; if units are different, ie. scale factor is referring to length while "size" refers to area, then you need to convert appropriately)

upper karma Jul 30, 2019, 4:22 AM

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so if I were to say I scaled down a figure by a ratio of 5:1 it would mean I’m making a new figure 5 times less in area?

spark stag Jul 30, 2019, 4:22 AM

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that's how i'd interpret that, yes

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well

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if you said you scaled down a figure's area

upper karma Jul 30, 2019, 4:23 AM

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Total eise*

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Size

spark stag Jul 30, 2019, 4:23 AM

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"size" is ambiguous

upper karma Jul 30, 2019, 4:23 AM

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Okay

spark stag Jul 30, 2019, 4:23 AM

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does it mean area or length?

upper karma Jul 30, 2019, 4:23 AM

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Like the whole figure

spark stag Jul 30, 2019, 4:23 AM

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...

upper karma Jul 30, 2019, 4:23 AM

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Including length and area

spark stag Jul 30, 2019, 4:23 AM

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ok so

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if we have a 5 * 5 square

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if we scale down the length according to a 5:1 ratio

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we get a 1*1 square

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whereas if we scale down the area

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we get a 2.236 * 2.236 square (since the area of 25 goes to 5, and the square root of 5 is about 2.236)

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there's a difference

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usually, when we say "scale factor"

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we're referring to length

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unless we say otherwise

upper karma Jul 30, 2019, 4:25 AM

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Doesn’t length affect area though?

spark stag Jul 30, 2019, 4:25 AM

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yes

upper karma Jul 30, 2019, 4:25 AM

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Okay

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If I were to say there was a figure and I were to make a new one from within in from the center and scale it down by a ratio of 1:0.93 the new figure will be 7% less in length?

queen python Jul 30, 2019, 4:28 AM

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Hmmm

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Anyone need help

upper karma Jul 30, 2019, 4:29 AM

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@spark stag am I Right or wrong?

spark stag Jul 30, 2019, 4:29 AM

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"scale it down by a ratio of 1:0.93"

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what are you scaling down

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the length? the area?

upper karma Jul 30, 2019, 4:30 AM

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Scale factor

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So length

spark stag Jul 30, 2019, 4:30 AM

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then yes

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it'll be 7% less in length.

worthy root Jul 30, 2019, 8:26 AM

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How angle between two parallel vectors be 0 .

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i mean they are parallel they wont even intersect ! then how the heck can one say the angle between them is 0.

keen aspen Jul 30, 2019, 8:27 AM

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The cross product of the two vectors are 0

worthy root Jul 30, 2019, 8:28 AM

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I have not learned cross products . @keen aspen

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WILL learn it next to next section

keen aspen Jul 30, 2019, 8:29 AM

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Well think of it like this, you have two lines intersecting at 90 degrees, what would happen to those lines if you would shift that angle to 0

worthy root Jul 30, 2019, 8:29 AM

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learn it in *

keen aspen Jul 30, 2019, 8:29 AM

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Or 180 degrees

worthy root Jul 30, 2019, 8:29 AM

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The angles between them is undefined

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They dont intersect . so no angle formed

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thinkingbread

quiet mason Jul 30, 2019, 8:51 AM

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u can say that the angle bw them is undefined

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it can be 0 or 180 or multiples of 180

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but in all cases sin180=0

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sin0=0

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sin(n*pi)=0

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n={0,infinity}

dark sparrow Jul 30, 2019, 8:55 AM

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p

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a

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r

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e

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n

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t

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h

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e

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s

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e

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s

quiet mason Jul 30, 2019, 9:08 AM

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sadcat

keen aspen Jul 30, 2019, 9:41 AM

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sin(1)80=0

dark sparrow Jul 30, 2019, 9:59 AM

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now that is just false

rich fiber Jul 30, 2019, 11:28 AM

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So the question is you have a 8 by 10 photo enlarged to an 18 by 22.5 inch phot what’s the scale factor

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I said 10:22.5 but the sender is 9:4, how??

cinder portal Jul 30, 2019, 11:32 AM

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take the larger side and divide by the smaller side

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doesn't that give you the scale factor?

rich fiber Jul 30, 2019, 11:34 AM

#

What larger side

#

Oh I’m dumb the awnser is 9 fourths I thought it was a ratio of 9 to4

worthy root Jul 30, 2019, 2:36 PM

#

I can make sense of angle between vectors with parallel shift of vector

queen python Jul 30, 2019, 3:32 PM

#

Anyone need help?

worthy root Jul 30, 2019, 5:52 PM

#

@queen python yes check #precalculus

dawn bobcat Jul 30, 2019, 10:10 PM

#

oy I'm studying for the SAT math test, can you guys explain this problem to me?

📎 unknown.png

trail minnow Jul 30, 2019, 10:11 PM

#

try grabbing a piece of paper and plotting 3,4 and 5,7 on it

dawn bobcat Jul 30, 2019, 10:11 PM

#

alright

#

when I look at this problem, I feel like 2 points can be on the border of an infinite amount of different circles

trail minnow Jul 30, 2019, 10:13 PM

#

do you know the equation of an ellipse?

dawn bobcat Jul 30, 2019, 10:14 PM

#

I'm a bit rusty, sorry

trail minnow Jul 30, 2019, 10:15 PM

#

it's $(\frac{x - x_c}{a})^2 - + (\frac{y - y_c}{b})^2 = 1$

somber coyoteBOT Jul 30, 2019, 10:15 PM

#

hegel:

📎 358385343629885440.png

trail minnow Jul 30, 2019, 10:15 PM

#

where a and b* are the foci of the ellipse

dawn bobcat Jul 30, 2019, 10:15 PM

#

ah you have a latex bot, beautiful

trail minnow Jul 30, 2019, 10:15 PM

#

yes uwu

#

so in this case a = b = r because a circle is a ellipse with 1 foci

#

so we can say $(\frac{x - x_c}{r})^2 - + (\frac{y - y_c}{r})^2 = 1$

somber coyoteBOT Jul 30, 2019, 10:15 PM

#

hegel:

📎 358385343629885440.png

trail minnow Jul 30, 2019, 10:16 PM

#

we can use this to determine the equation of the circle, no?

#

as we have two points

#

o wait im super rusty, this might not be correct tinktonk

sleek tangle Jul 30, 2019, 10:16 PM

#

wouldnt you have multiple circle equations that are satisfied by those points?

mental wharf Jul 30, 2019, 10:16 PM

#

you need 3 points

dawn bobcat Jul 30, 2019, 10:17 PM

#

^ I agree with sigma

sleek tangle Jul 30, 2019, 10:17 PM

#

it does work

mental wharf Jul 30, 2019, 10:17 PM

#

any 3 points that arent in a line form a unique circle

trail minnow Jul 30, 2019, 10:17 PM

#

ye

sleek tangle Jul 30, 2019, 10:17 PM

#

https://www.geogebra.org/resource/zGW6B389/3ntd7CHEAtXLzFSh/material-zGW6B389-thumb@l.png

dawn bobcat Jul 30, 2019, 10:17 PM

#

this might be a super shitty question

mental wharf Jul 30, 2019, 10:17 PM

#

so, find a point that makes a line with the 2 points you have

dawn bobcat Jul 30, 2019, 10:17 PM

#

I got it from an unofficial test

trail minnow Jul 30, 2019, 10:17 PM

#

thonkzoom

#

yeah this works for 3 points but not 2

hard gale Jul 30, 2019, 10:17 PM

#

clandestine testing

mental wharf Jul 30, 2019, 10:18 PM

#

because then you cant make a circle

#

its just a line

trail minnow Jul 30, 2019, 10:18 PM

#

what the fok

hard gale Jul 30, 2019, 10:18 PM

#

maybe it's from a 1995 sat who knows

trail minnow Jul 30, 2019, 10:18 PM

#

oh wait

dawn bobcat Jul 30, 2019, 10:18 PM

#

question: does "lies on" mean contained in the circle or on the border of the circle?

mental wharf Jul 30, 2019, 10:18 PM

#

border

upper karma Jul 30, 2019, 10:18 PM

#

Well you can't have a point on the line between the two points

trail minnow Jul 30, 2019, 10:18 PM

#

border

dawn bobcat Jul 30, 2019, 10:18 PM

#

ah shite

trail minnow Jul 30, 2019, 10:18 PM

#

yeah

dawn bobcat Jul 30, 2019, 10:18 PM

#

there it is

trail minnow Jul 30, 2019, 10:18 PM

#

i was gonna say find the line between the two points

upper karma Jul 30, 2019, 10:18 PM

#

Without blowing up radius to infinite

mental wharf Jul 30, 2019, 10:18 PM

#

a disk is the points inside

#

a circle is the boundary

dawn bobcat Jul 30, 2019, 10:19 PM

#

I thought about sigma's solution but I misunderstood what lies on meant

trail minnow Jul 30, 2019, 10:19 PM

#

@dawn bobcat try calculating the line between P_1 and P_2 (our given points) and seeing if any of those points lie on them

dawn bobcat Jul 30, 2019, 10:19 PM

#

so what then, you find the equation of the line between those two points and then plug in all answers until one is on the line?

trail minnow Jul 30, 2019, 10:19 PM

#

ye

mental wharf Jul 30, 2019, 10:19 PM

#

i just extended the line first

#

and then check the other points

dawn bobcat Jul 30, 2019, 10:20 PM

#

I got line y = 1.5x - 0.5

upper karma Jul 30, 2019, 10:20 PM

#

See if the pairs lie on the line

dawn bobcat Jul 30, 2019, 10:21 PM

#

E is the answer btw

upper karma Jul 30, 2019, 10:21 PM

#

Looks right to me

trail minnow Jul 30, 2019, 10:21 PM

#

ye it is

dawn bobcat Jul 30, 2019, 10:21 PM

#

ye E is on the line

trail minnow Jul 30, 2019, 10:21 PM

#

you can just plot it and see

dawn bobcat Jul 30, 2019, 10:21 PM

#

ok I misunderstood what lies on meant

#

sucks

trail minnow Jul 30, 2019, 10:21 PM

#

oof

#

nbd

mental wharf Jul 30, 2019, 10:22 PM

#

👍

dawn bobcat Jul 30, 2019, 10:22 PM

#

I just joined this server btw, is it better to ask questions in math help or pre-university channels?

hard gale Jul 30, 2019, 10:23 PM

#

we don't care tbh

sleek tangle Jul 30, 2019, 10:23 PM

#

couldnt you still have a point that's not on the line but that's on the circle?

dawn bobcat Jul 30, 2019, 10:23 PM

#

I'ma migrate to the math help channels for my next like 12 questions

upper karma Jul 30, 2019, 10:23 PM

#

All points that could lie on a circle are off that line

sleek tangle Jul 30, 2019, 10:24 PM

#

ah yeah right

whole swift Jul 31, 2019, 2:07 AM

#

📎 unknown.png

#

📎 unknown.png

#

Can anybody help me wit this geometry question
By this definition of cone how do I solve this?

queen python Jul 31, 2019, 3:07 AM

#

@whole swift i think this is calc

minor arch Jul 31, 2019, 9:48 AM

#

https://cdn.discordapp.com/attachments/455527586131476480/606053225941958667/Screenshot_20190731-041810_Chrome.jpg

#

How would I solve this?

cinder portal Jul 31, 2019, 9:51 AM

#

draw it first

#

and see what you have so far

#

there is a very specific formula for finding the angle between two lines in cartesian plane, kinda forgot it

#

but see if there is something obvious, like maybe they're perpendicular or something

minor arch Jul 31, 2019, 9:59 AM

#

I got 1.12 degrees. @cinder portal

#

Can you confirm?

cinder portal Jul 31, 2019, 10:00 AM

#

what formula did you use?

#

There's a specific formula relating to tan(theta) = something something

#

i forgot

#

ah fuck it lemme check using vectors

dark sparrow Jul 31, 2019, 10:01 AM

#

1.12 degrees sounds like way too little

cinder portal Jul 31, 2019, 10:02 AM

#

$\cos(\theta) = \frac{8}{\sqrt{65}}$

somber coyoteBOT Jul 31, 2019, 10:02 AM

#

MemesPlease:

📎 190017172074921986.png

cinder portal Jul 31, 2019, 10:02 AM

#

is what i got

minor arch Jul 31, 2019, 10:02 AM

#

I did. Tan theta = (8-7)/(1+8*7)

dark sparrow Jul 31, 2019, 10:02 AM

#

,calc atan(1/8) * 180/pi

somber coyoteBOT Jul 31, 2019, 10:03 AM

#

Result:

7.1250163489018

cinder portal Jul 31, 2019, 10:05 AM

#

,w arccos(8/(65)^(1/2))

somber coyoteBOT Jul 31, 2019, 10:05 AM

#

📎 wolf.png

Display results online and refine query

cinder portal Jul 31, 2019, 10:06 AM

#

,calc 0.12345499 * 180/pi

somber coyoteBOT Jul 31, 2019, 10:06 AM

#

Result:

7.0734498868298

cinder portal Jul 31, 2019, 10:06 AM

#

close

dark sparrow Jul 31, 2019, 10:10 AM

#

you do realize the parens around 65 were redundant there

#

right

cinder portal Jul 31, 2019, 10:11 AM

#

wasnt sure how to type it, just wanted to make sure LOL

minor arch Jul 31, 2019, 10:11 AM

#

I used ad ifferent method this time.

#

51.6 degrees work?

What I did this time was just measure the distance between each point and apply Pythagorean to get the value for each line. Then I used the inverse of cos to get the degree. Too complicated?

cinder portal Jul 31, 2019, 10:14 AM

#

did u draw it?

#

try eyeballing it and see if it looks like 51.6 degree

minor arch Jul 31, 2019, 10:19 AM

#

It doesn't.

#

I just need to see if my formulas are correct.

keen glen Jul 31, 2019, 10:20 AM

#

someone teach me how to maths

drowsy spoke Jul 31, 2019, 1:04 PM

#

practice

#

lots of it

#

and when you think you've got enough

#

do more

small raptor Jul 31, 2019, 1:12 PM

#

Then cry

worthy root Jul 31, 2019, 1:37 PM

#

REEEE weSmart

frail depot Jul 31, 2019, 2:03 PM

#

and libgen books

upper karma Jul 31, 2019, 2:56 PM

#

for solving sinusodidal model word problems:
why is it for sin, you do sin(theta)=sin(pi-theta) and then for cos, you do cos(theta)=cos(2pi-theta) to find the 2nd solution

like why do you different things depending on if its sin or cos.

p.s: just trying to understand the meaning behind this

dark sparrow Jul 31, 2019, 3:02 PM

#

because sin and cos are different functions and have different symmetries

digital stirrup Jul 31, 2019, 3:02 PM

#

Hey @upper karma, it all has to do with the unit circle. Remember that cosine and sine can be represented as the x and y values respectively as you travel along a unit circle's circumference with radius 1.

#

check out this graphic:

📎 unit-circle-sin-cos-tan.png

#

So, since sine is the y-value for a given angle along the unit circle, think about what angles produce the same exact height, or y-value, as each other

#

Say we have an angle x degrees along the unit circle. The terminal point of the angle has coordinates (cos x, sin x). So what if we started at the 180 degree mark, and traveled clockwise (negative angle) by x degrees? It's just a reflection of our original angle x across the y-axis. Therefore, the heights are the same. Another word for "start at 180 degrees and move backwards by the original angle) is (pi - theta), since pi radians = 180 degrees and (-theta) means move backwards/clockwise by theta

#

here's a better photo:

📎 unknown.png

#

You can think about the same think for the cosine function. For the cosine, to get an equal x-value, you can go around 360 degrees (+2pi radians) and then subtract your angle (-theta), so you are basically just reflecting your original angle across the x-axis. This results in the terminal point of your new angle having the same cosine, or x-coordinate, as the terminal point of your original angle. Hope this helps 😃

upper karma Jul 31, 2019, 5:26 PM

#

thanks for the help 😁

digital stirrup Jul 31, 2019, 5:29 PM

#

No prob 😃

gusty drum Jul 31, 2019, 5:52 PM

#

creeper aww masn

upper karma Jul 31, 2019, 7:55 PM

#

Anyone here ? I really need some urgent help.

#

@upper karma

#

what do you need

#

Hello there

#

Just a sec

#

📎 image0.jpg

#

Should nt sin square (A/2) be 2 sin square (A/2) ?

#

I think its a typo or something ?

#

Because the 2 reappears in the deriviation

chrome fiber Jul 31, 2019, 8:04 PM

#

yeah it should say 2sin^2(A/2)

upper karma Jul 31, 2019, 8:05 PM

#

it should?

#

theres a 4 on the right side

#

Wait

chrome fiber Jul 31, 2019, 8:05 PM

#

thats from the 2(s - b) and 2(s - c)?

upper karma Jul 31, 2019, 8:06 PM

#

Oh yes !

#

are u asking about the so to therefor line

#

then its correct, 2 on the left and 4/2 on the right

chrome fiber Jul 31, 2019, 8:06 PM

#

theyre asking about the first one

#

im assuming

upper karma Jul 31, 2019, 8:06 PM

#

Asking about the first one

chrome fiber Jul 31, 2019, 8:06 PM

#

https://puu.sh/DZHiJ/cc44e4a9a9.png

#

bc thats not true for all A.

upper karma Jul 31, 2019, 8:07 PM

#

ah okay

#

Thanks guys

#

I was assuming that i was seeing things because of being sleepy

#

And yes i have 1 more question

chrome fiber Jul 31, 2019, 8:08 PM

#

yes?

upper karma Jul 31, 2019, 8:09 PM

#

Why should Sin(a/2) be always positive ?

#

Oh i got it we are dealing with triangles

#

So a/2 should be less than 90 deg ? Right ?

chrome fiber Jul 31, 2019, 8:10 PM

#

it doesnt matter if its less than 90

#

any angle of a triangle < pi

upper karma Jul 31, 2019, 8:11 PM

#

Yes but i dont we have negative angles in triangles ?

chrome fiber Jul 31, 2019, 8:11 PM

#

and you should know that sin(x) for x < pi is positive

digital stirrup Jul 31, 2019, 8:11 PM

#

Oh sorry, I didn't realize we were just talking about triangles

upper karma Jul 31, 2019, 8:11 PM

#

*think

#

@chrome fiber doesnot it depend on the quadrants ?

chrome fiber Jul 31, 2019, 8:12 PM

#

it does, but think about it

#

you can always choose coordinate axes such that the angle lies between 0 and pi

upper karma Jul 31, 2019, 8:13 PM

#

you can always choose a coordinate axis such that the angle lies between 0 and pi , .jun can you elaborate this more .0?

chrome fiber Jul 31, 2019, 8:14 PM

#

like

#

put y = 0 on one arm

#

and sweep the angle from there

#

it will always be in the first and/or second quadrant

#

cant be more than that, since all angles in a triangle are less than pi

upper karma Jul 31, 2019, 8:15 PM

#

Oh yes !

#

Yes

#

Thanks a lot @chrome fiber for providing immediate help, wonder what time it is for you but for me its good night !

chrome fiber Jul 31, 2019, 8:16 PM

#

np

digital stirrup Jul 31, 2019, 9:37 PM

#

Hello @upper karma , look at angle BAC and x. When added together, they form a line, right? We call these supplementary angles, which means that the two angles add up to 180 degrees. So angle BAC + angle PAB = 180 degrees. Now, remember that the sum of the angles inside a triangle is also 180 degrees. See if you can use these facts to find out more about the relation between angle PAB and angle ACB, using supplementary angles and the fact that the interior angles of a triangle sum to 180.Let me know if that helps, or if you want me to go into more detail.

lusty quest Jul 31, 2019, 9:37 PM

#

how come i could figure out the angle for A using the SSA formula, but then get the wrong answer for C, which I also used the SSA formula

(5.69sin27.9)/2.7195 = 7225

📎 unknown.png

#

idk what the Mx + N means

digital stirrup Jul 31, 2019, 9:39 PM

#

See what happens when you subtract 90 from both sides

#

x = 90 + ACB, so ACB = x - 90

lusty quest Jul 31, 2019, 9:40 PM

#

the question is asking for Mx + N

digital stirrup Jul 31, 2019, 9:40 PM

#

This is in the form Mx + N, where M = 1 and N = -90

#

So M + N = -89

lusty quest Jul 31, 2019, 9:42 PM

#

calm down euler

digital stirrup Jul 31, 2019, 9:42 PM

#

I'm sorry if I haven't been clear, we can take it to dms if you want

#

Since we can represent the measure of ACB as x - 90, and we are given that the measure of ACB can be represented by some equation Mx + N, where m is set to 1 and N is some other number, that other number must be -90, since the measure of ACB is proven to be x -90. So M + N = 1 + (-90) = -89. Hope that helps

woeful monolith Jul 31, 2019, 9:44 PM

#

yo

#

is probability in algebra?

lusty quest Jul 31, 2019, 9:44 PM

#

yeah

#

just a little bit

woeful monolith Jul 31, 2019, 9:45 PM

#

ok thx i got a little confused because i learned about probability in my geomtry class

lusty quest Jul 31, 2019, 9:45 PM

#

damn that math teacher

woeful monolith Jul 31, 2019, 9:46 PM

#

lol

digital stirrup Jul 31, 2019, 10:11 PM

#

Hey @lusty quest , it's possible to get the wrong answer for C if you are using the Law of Sines to figure out C. For example, say you used the law of sines to find that Side B = 2.7915 meters. You could now set up the proportion Sine 27.9 / 2.7915 = Sine C / 5.69. Cross-multiplication gets you to Sine C = 0.954. To find out what the measure of C is, you probably used the inverse sine function on your calculator, and it gave you C = 72.5 degrees. However, the inverse sine function is only defined for values from -90 degrees to +90 degrees, so no matter what it will always return an acute angle. In cases like these, you just have to remember that there are acute and obtuse angles with the same sine value, and it's up to you to find out which one to use based on the side lengths and the fact that the angles in a triangle must add up to 180. It's all in the rule sin (180 - x) = sin (x). In addition, the angle that creates the biggest side in a triangle must also be the biggest angle. Since c is the biggest side, C must also be the biggest angle. If C = 72.5 and B = 27.9, then A would have to be 79.6, and A would be the biggest angle. But a is not the biggest side, so A can't be the biggest angle. That means that instead of using the acute C given to you by the inverse sine function, you have to use the obtuse C with the same sine as the acute angle given you by the inverse sine function. So that would be 180 - 72.5, or 107.5 degrees for C. And 107.5 + 27.9 + 44.6 = 180, so it all checks out. C is the biggest angle and c is the biggest side, A is the second biggest angle and a is the second biggest side, and B is the smallest angle and b is the smallest side, so that checks out as well. Hope this helps 😃

lusty quest Jul 31, 2019, 10:22 PM

#

holy crap, thanks for the answer

digital stirrup Jul 31, 2019, 10:31 PM

#

You're welcome 😃

echo trench Aug 1, 2019, 12:41 AM

#

📎 a_problem.PNG

#

Any help with this?

#

(Also by help I mean, learn how to solve it too)

#

I strive for the intelligence tinktonk

wind imp Aug 1, 2019, 12:42 AM

#

so uh can you figure out the angle thats between D and the right angle?

echo trench Aug 1, 2019, 12:43 AM

#

You mean opposite of right angle

#

*90 degrees

wind imp Aug 1, 2019, 12:43 AM

#

ok C first i guess

#

youve found that one, right?

echo trench Aug 1, 2019, 12:43 AM

#

No

wind imp Aug 1, 2019, 12:43 AM

#

(i initially meant the one without a label)

echo trench Aug 1, 2019, 12:43 AM

#

I have not

#

Aha

spark stag Aug 1, 2019, 12:45 AM

#

if we have this

#

📎 unknown.png

#

what's C?

echo trench Aug 1, 2019, 12:45 AM

#

Oh

#

90 degrees

#

aha

spark stag Aug 1, 2019, 12:45 AM

#

right, and you can see how this applies to your diagram

#

since the dotted line is at 90 degrees from the slanted one

echo trench Aug 1, 2019, 12:46 AM

#

alright

#

got that down

spark stag Aug 1, 2019, 12:46 AM

#

next, do you know how many degrees are in a triangle?

echo trench Aug 1, 2019, 12:46 AM

#

the holy 180

spark stag Aug 1, 2019, 12:46 AM

#

yes

#

can we use that to fill in any angles?

echo trench Aug 1, 2019, 12:46 AM

#

can we subtract 90 from it?

#

wait no

#

the 47

#

*37

spark stag Aug 1, 2019, 12:47 AM

#

if we look at this triangle

📎 unknown.png

#

we know two of its angles:

#

angle theta (37 degrees)

#

and the right angle (90 degrees)

#

we can use this to find the missing angle

echo trench Aug 1, 2019, 12:48 AM

#

Ok so

#

the 90 degrees that we found, opposite

#

is that applying there

spark stag Aug 1, 2019, 12:48 AM

#

📎 unknown.png

echo trench Aug 1, 2019, 12:48 AM

#

ah

#

thank

#

so that means

#

that last angle is 53

#

and then if I remember, the 53 and its opposite need to equal 90

#

which is 37

spark stag Aug 1, 2019, 12:50 AM

#

what is "its opposite"?

echo trench Aug 1, 2019, 12:51 AM

#

Angle D

spark stag Aug 1, 2019, 12:52 AM

#

ah, yes

echo trench Aug 1, 2019, 12:52 AM

#

Now question

spark stag Aug 1, 2019, 12:52 AM

#

since when we add those together

#

we should get a right angle

echo trench Aug 1, 2019, 12:52 AM

#

Yes

#

Now

#

Where do i go form there

#

*from

spark stag Aug 1, 2019, 12:52 AM

#

📎 unknown.png

echo trench Aug 1, 2019, 12:52 AM

#

AHHH

#

okkkkkkk

spark stag Aug 1, 2019, 12:53 AM

#

er

#

that should be a 53

#

but yeah

echo trench Aug 1, 2019, 12:53 AM

#

No i got it

#

thanks for visuals

#

Now i need to figure out what b and a are

#

but

spark stag Aug 1, 2019, 12:54 AM

#

this might help

📎 unknown.png

echo trench Aug 1, 2019, 12:54 AM

#

Isnt it just what is opposite

#

😄

spark stag Aug 1, 2019, 12:54 AM

#

yeah, essentially

#

since it still adds up to 90 degrees

#

and the angle between the lines is preserved

#

(the lines dont bend or curve or anything)

echo trench Aug 1, 2019, 12:55 AM

#

So thats set wow

#

ahh

#

I understand it now

spark stag Aug 1, 2019, 12:55 AM

#

aside: if you take high school physics, this exact diagram comes up when modelling the forces on an object on an inclined plane

#

and the fact that angle theta = angle D (as labelled here) is important

echo trench Aug 1, 2019, 12:57 AM

#

Oh wow, dude that is exactly why im doing this

#

AP Physics 1 time

#

Oh wtf

#

theta is equal to angle d and a

#

oh wow

spark stag Aug 1, 2019, 12:58 AM

#

yep, and that holds no matter what theta is

echo trench Aug 1, 2019, 12:58 AM

#

cool

spark stag Aug 1, 2019, 12:58 AM

#

(as long as its less than 90 degrees)

echo trench Aug 1, 2019, 12:58 AM

#

Hey namington how solid are u with with the trig unit circle

trail minnow Aug 1, 2019, 12:59 AM

#

namington is a grad student in math mniip

#

i would be somewhat worried if he couldn't handle the unit circle

spark stag Aug 1, 2019, 12:59 AM

#

in fairness, i havent used the unit circle in, like, a decade (outside of tutoring)

#

but yes, I am familiar with it.

echo trench Aug 1, 2019, 12:59 AM

#

I dont get it and what the hecky its asking

spark stag Aug 1, 2019, 1:00 AM

#

essentially, the unit circle is used to visually find trigonometric values of a certain angle

echo trench Aug 1, 2019, 1:00 AM

#

📎 Capture.PNG

#

Ok

spark stag Aug 1, 2019, 1:00 AM

#

the key insight is that

#

the sine of an angle represents its "y" value

#

and the cosine represents its "x" value

#

moreover, the radius of the circle is 1

#

thats why we call it the "unit" circle - "unit" meaning 1 (think "uno")

echo trench Aug 1, 2019, 1:01 AM

#

or uni

spark stag Aug 1, 2019, 1:01 AM

#

sure

echo trench Aug 1, 2019, 1:01 AM

#

m

spark stag Aug 1, 2019, 1:01 AM

#

let's start with the 0 degrees, for example

echo trench Aug 1, 2019, 1:01 AM

#

ok

spark stag Aug 1, 2019, 1:01 AM

#

whats the x value of that point?

echo trench Aug 1, 2019, 1:02 AM

#

uh

#

0

spark stag Aug 1, 2019, 1:02 AM

#

not quite

echo trench Aug 1, 2019, 1:02 AM

#

darn

spark stag Aug 1, 2019, 1:02 AM

#

remember that the radius is 1

echo trench Aug 1, 2019, 1:02 AM

#

so 1?

spark stag Aug 1, 2019, 1:02 AM

#

right

#

like this

📎 unknown.png

echo trench Aug 1, 2019, 1:02 AM

#

mm

spark stag Aug 1, 2019, 1:02 AM

#

now, the x value represents the cosine of that angle

#

I'll give you a quick justification of why that's true in a minute

#

whats the y value of this point of 0 degrees?

#

(i'm saying "the point at 0 degrees", but i really mean the point where that arm intersects the circle - you get the idea, though)

echo trench Aug 1, 2019, 1:04 AM

#

am lost

spark stag Aug 1, 2019, 1:05 AM

#

whats the y value of the pink point here?

📎 unknown.png

echo trench Aug 1, 2019, 1:05 AM

#

1

spark stag Aug 1, 2019, 1:05 AM

#

"y" means vertical, right?

#

up and down

#

so the y value of the pink point should be 0

echo trench Aug 1, 2019, 1:06 AM

#

o

spark stag Aug 1, 2019, 1:06 AM

#

so the pink point, 0 degrees, has an x value of 1, and a y value of 0

#

ie, its the point (1,0)

echo trench Aug 1, 2019, 1:06 AM

#

So (1,0)

spark stag Aug 1, 2019, 1:06 AM

#

yep

#

i'm gonna skip ahead to 90 degrees next

#

because it's very similar

echo trench Aug 1, 2019, 1:06 AM

#

and thats cos

spark stag Aug 1, 2019, 1:07 AM

#

whats the coordinate of the point at 90 degrees?

echo trench Aug 1, 2019, 1:07 AM

#

1

#

(1,1)

#

no

#

(0,1)

spark stag Aug 1, 2019, 1:07 AM

#

right

#

so we have two points

#

0 degrees is (1,0)
90 degrees is (0,1)

#

now, the cosine of an angle is its x value

#

and the sine is its y value

#

so whats the cosine of 0 degrees?

echo trench Aug 1, 2019, 1:08 AM

#

1

spark stag Aug 1, 2019, 1:08 AM

#

right, and its sine?

echo trench Aug 1, 2019, 1:11 AM

#

0

#

oh wait

#

is it?

spark stag Aug 1, 2019, 1:11 AM

#

thats correct

echo trench Aug 1, 2019, 1:11 AM

#

i just filled out for cos for 0 degrees

spark stag Aug 1, 2019, 1:11 AM

#

the cosine of 0 degrees is 1

#

and the sine of 0 degrees is 0

#

in other words, if we have an angle theta, its ordered pair (x, y) represents (cosine(theta), sine(theta))

#

fill out the values of cosine/sine of 90 degrees in the same way that you did 0

echo trench Aug 1, 2019, 1:13 AM

#

(0,1)

spark stag Aug 1, 2019, 1:13 AM

#

yep

#

so we should end up with

#

this

📎 unknown.png

echo trench Aug 1, 2019, 1:14 AM

#

ahh

#

now

#

the otehrs

spark stag Aug 1, 2019, 1:14 AM

#

right

#

for these, its probably best to draw them as a right triangle

#

I'm gonna start iwth 30 degrees

echo trench Aug 1, 2019, 1:15 AM

#

wtf

spark stag Aug 1, 2019, 1:15 AM

#

something like this

📎 unknown.png

#

(ignore the top-left bit, screenshotting is hard)

#

or, drawn on your diagram

📎 unknown.png

echo trench Aug 1, 2019, 1:16 AM

#

So i draw that on the unit circle or on the side

#

done

spark stag Aug 1, 2019, 1:17 AM

#

let me fill in the angles we know

📎 unknown.png

echo trench Aug 1, 2019, 1:17 AM

#

where do i go from here?

spark stag Aug 1, 2019, 1:17 AM

#

and we know our last angle will be 60 degrees, but that doesnt really matter

#

now, we need to make an insight here

#

remember that the radius of the circle is 1

#

now notice that the diagonal slant of the triangle connects from the center to the edge of the circle

#

a line from the center to the edge... is a radius

#

so that diagonal line is 1

#

📎 unknown.png

#

this should make it clear why cosine corresponds to x and sine corresponds to y, by the way

#

the x side is the adjacent (cosine is adjacent/hypotenuse, which will be x/1 = x)

#

and the y side is opposite (sine = opposite/hypotenuse = y/1 = y)

#

now, we just need to find the values for x and y

#

and those'll give us our sine/cosine

#

do you know how to construct a 30-60-90 degree triangle?

echo trench Aug 1, 2019, 1:21 AM

#

oh yeah

spark stag Aug 1, 2019, 1:22 AM

#

we take a 60-60-60 triangle, where all the sides are 1

📎 unknown.png

echo trench Aug 1, 2019, 1:23 AM

#

ok

spark stag Aug 1, 2019, 1:23 AM

#

and cut it in half

📎 unknown.png

#

this cuts one of the 60 degree angles into 30 degrees, and makes a 90 degree angle

#

and it also cuts one of the sides into 1/2

echo trench Aug 1, 2019, 1:24 AM

#

ok

spark stag Aug 1, 2019, 1:24 AM

#

and with pythagoreans theorem, we can find the third side

📎 unknown.png

#

quick derivation:

#

a^2 + b^2 = c^2

#

b^2 = c^2 - a^2

#

b^2 = (1)^2 - (1/2)^2

#

b^2 = 1 - 1/4
b ^2 = 3/4
b = sqrt(3)/2

#

oops, i typod in my image; thats supposed to be sqrt(3)/2

#

not sqrt(2)/2

#

regardless

#

we can apply this to the triangle we drew on our unit circle

#

"rotate" it so the 30 degrees lines up, and we can see:

#

📎 unknown.png

#

x = sqrt(3)/2

#

y = 1/2

#

so now we know

#

the point of 30 degrees

#

is $\left(\frac{\sqrt{3}}{2} , \frac12\right)$

somber coyoteBOT Aug 1, 2019, 1:27 AM

#

Namington:

📎 105878844061286400.png

spark stag Aug 1, 2019, 1:27 AM

#

and again, the cosine is the x value, and the sine is the y value

#

so you should be able to fill out those values for 30 degrees now

#

this might seem like a lot of work - and it is. that's why we have the unit circle as a memorization tool

#

rather than having to go through the triangle proof each time

#

that said, now that we've done 30 degrees, we can do 60 degrees really quickly

echo trench Aug 1, 2019, 1:28 AM

#

easier way 😄

spark stag Aug 1, 2019, 1:28 AM

#

since the same triangle applies

echo trench Aug 1, 2019, 1:29 AM

#

oh

spark stag Aug 1, 2019, 1:30 AM

#

📎 unknown.png

#

so its coordinate is (1/2, sqrt(3)/2)
you'll note that its the same as 30 degrees, just "flipped around"

echo trench Aug 1, 2019, 1:30 AM

#

i didnt comprehend all that

#

im sorry

spark stag Aug 1, 2019, 1:31 AM

#

the gist is this:

#

we construct a 30-60-90 degree triangle

#

and can see that it looks like this

📎 unknown.png

#

by putting this triangle into the unit circle so that it matches up with our angles

#

we can find that angle's x and y value

#

[nitpick: the x and y value where that angle's arc intersects the unit circle]

#

if we flip and rotate this triangle to fit it into 30 degrees

#

it fits in like this

📎 unknown.png

#

oh, by the way, i meant sqrt(3)/2, not sqrt(2)/2

#

typod in the yellow image

#

anyway

#

from this drawing, we can see that side x = sqrt(3)/2

#

and side y = 1/2

#

so the coordinate that corresponds to 30 degrees

#

is $\left(\frac{\sqrt{3}}{2} , \frac12\right)$

somber coyoteBOT Aug 1, 2019, 1:33 AM

#

Namington:

📎 105878844061286400.png

spark stag Aug 1, 2019, 1:34 AM

#

we can also fit in the 30-60-90 triangle into our 60 degree angle, with another rotation. doing that gets us this

📎 unknown.png

#

note that the x side is 1/2 now

#

and the y side is sqrt(3)/2

#

this is "backwards" from 30 degrees

#

like how 0 and 90 were "backwards" from each other

#

so the coordinate that corresponds to $60^{\circ}$ is $\left(\frac12, \frac{\sqrt{3}}{2}\right)$

somber coyoteBOT Aug 1, 2019, 1:35 AM

#

Namington:

📎 105878844061286400.png

spark stag Aug 1, 2019, 1:35 AM

#

again, "backwards" from 30 degrees

#

do you mostly follow that?

echo trench Aug 1, 2019, 1:36 AM

#

Ok where did 1/2 and square roo 3/2 come from

spark stag Aug 1, 2019, 1:37 AM

#

the construction of the 30-60-90 degree triangle

#

lets say we started with an equilateral triangle. in an equilateral triangle, all sides and angles are the same. this means the angles must be 60 (since 60 * 3 = 180). let's let the sides be 1.

📎 unknown.png

#

now lets say we cut it in half, like this. Cutting a 60 degree angle in half gives us a 30 degree angle, and cutting a side of length 1 in half gives us a side of length 1/2

📎 unknown.png

#

the reason we do this cut is to get a 30-60-90 triangle

#

now the last step is to find the missing side, the dotted line

#

and we do this via pythagorean theorem

#

if we call that side "b"

#

then 1/2 is "a" and 1 is "c"

#

so $a^2 + b^2 = c^2 \ b^2 = c^2 - a^2 \ b^2 = (1)^2 - (1/2)^2 \ b^2 = 1 - \frac14 \ b^2 = \frac34 \ b = \frac{\sqrt{3}}{\sqrt{4}} = \frac{\sqrt{3}}{2}$

somber coyoteBOT Aug 1, 2019, 1:42 AM

#

Namington:

📎 105878844061286400.png

spark stag Aug 1, 2019, 1:42 AM

#

hence, the third side is sqrt(3)/2

#

so our 30-60-90 unit triangle looks like this.

📎 unknown.png

#

we can actually use this to find the sine, cosine, and tangent of 30 degrees and 60 degrees

#

or we can use it to make the unit circle, as i showed above

#

which helps us memorize these values

#

instead of using the triangle itself to derive them

echo trench Aug 1, 2019, 6:48 PM

#

@spark stag Sorry for late response, power went out but hmmmm

glad ocean Aug 1, 2019, 7:02 PM

#

pOwEr wEnT oUt

echo trench Aug 1, 2019, 7:05 PM

#

@glad ocean ok...

#

@spark stag Yeah I think i got an understanding actually now

vocal jewel Aug 1, 2019, 8:00 PM

#

if i have the hypot of a triangle, is there a way to get the other 2 sides ?

spark stag Aug 1, 2019, 8:00 PM

#

do you have any other information?

#

such as its angles?

vocal jewel Aug 1, 2019, 8:01 PM

#

umm... i have the 2 points of the hypot

#

let me draw it real quick

#

📎 unknown.png

spark stag Aug 1, 2019, 8:03 PM

#

seems like you have the two sides?

#

both are 50

vocal jewel Aug 1, 2019, 8:03 PM

#

yes...but pretend those are not there.. lol

spark stag Aug 1, 2019, 8:04 PM

#

well, if you know the two sides are equal

#

then you can use pythagorean theorem

#

a^2 + b^2 = c^2

#

a = b, so

#

2a^2 = c^2

#

solve for a

#

c/sqrt(2) = a

#

trying this with the diagram, we get

#

,calc 70.71/sqrt(2)

somber coyoteBOT Aug 1, 2019, 8:05 PM

#

Result:

49.999520497701

spark stag Aug 1, 2019, 8:05 PM

#

which checks out

#

"the two sides are equal" is part of that "other information" I was talking about earlier, btw

vocal jewel Aug 1, 2019, 8:06 PM

#

nice!

#

i'm trying to think if I will always have 2 equal sides of a triangle

#

yea.. I will... Thank you very much!!

rigid wharf Aug 1, 2019, 10:14 PM

#

A segment is created from points A and B. To copy segment AB, which of the following needs to be identified for the construction?

a) The distance between point A and a point not on the segment
b) The midpoint of points A and B
c) The midpoint between point B and a point not on the segment
d) The distance between points A and B

#

I think its D but I am not sure

spark stag Aug 1, 2019, 10:15 PM

#

when we copy a segment

#

we need to make a new segment with the same length, right?

#

the only one of those that lets us find length is D

#

so yeah, D is correct.

rigid wharf Aug 1, 2019, 10:17 PM

#

Thank you

upper karma Aug 2, 2019, 1:42 AM

#

Stupid question but I am struggling to find qx and xy

📎 image0.jpg

#

I know they’re congruent

fossil ledge Aug 2, 2019, 1:43 AM

#

is PX 15cm or PQ?

queen python Aug 2, 2019, 1:46 AM

#

Anyone need help?

upper karma Aug 2, 2019, 1:46 AM

#

Yes, check above

#

@fossil ledge px is 15

#

I know the theorem that two tangents off the same end point of the same circle are congruent

#

but I’m lost on finding the other two segments

queen python Aug 2, 2019, 1:47 AM

#

Isint qx 17

fossil ledge Aug 2, 2019, 1:47 AM

#

This is somewhere in my head, but I havent done this in a long time

queen python Aug 2, 2019, 1:47 AM

#

Wait no

fossil ledge Aug 2, 2019, 1:47 AM

#

dont just give answers bongo boi

#

work it through with them

upper karma Aug 2, 2019, 1:48 AM

#

qx can’t be 17

queen python Aug 2, 2019, 1:48 AM

#

It's wrong

upper karma Aug 2, 2019, 1:48 AM

#

I know the concept

queen python Aug 2, 2019, 1:48 AM

#

Ok

fossil ledge Aug 2, 2019, 1:48 AM

#

my point still stands, work it through with them

queen python Aug 2, 2019, 1:48 AM

#

Lemme explain

upper karma Aug 2, 2019, 1:48 AM

#

👌

#

I'm studying anyway

queen python Aug 2, 2019, 1:48 AM

#

What is yr

upper karma Aug 2, 2019, 1:48 AM

#

17

queen python Aug 2, 2019, 1:48 AM

#

Good

olive solar Aug 2, 2019, 1:49 AM

#

thonkzoom

queen python Aug 2, 2019, 1:49 AM

#

Can you tell me why?

upper karma Aug 2, 2019, 1:49 AM

#

lol that’s the easy theorem

#

I just said

#

I know the theorem that two tangents off the same end point of the same circle are congruent

queen python Aug 2, 2019, 1:49 AM

#

thonkeyes

#

the kids these days are so smart

upper karma Aug 2, 2019, 1:50 AM

#

I’m no idiot dude

queen python Aug 2, 2019, 1:50 AM

#

Good for you

upper karma Aug 2, 2019, 1:51 AM

#

..alright I’ll just skip it for now

#

thanks for the help

queen python Aug 2, 2019, 1:52 AM

#

Np

#

@upper karma

#

Is that the whole problém?

upper karma Aug 2, 2019, 1:54 AM

#

indeed that is The whole problem

fossil ledge Aug 2, 2019, 1:54 AM

#

you asked if anyone needed help

#

and then made fun of him

upper karma Aug 2, 2019, 1:54 AM

#

I’m not phased

#

don’t worry about it

queen python Aug 2, 2019, 1:54 AM

#

When did I make fun of him

upper karma Aug 2, 2019, 1:55 AM

#

oh wait

fossil ledge Aug 2, 2019, 1:55 AM

#

well I cant get offended on your behalf, but like bruh

upper karma Aug 2, 2019, 1:55 AM

#

I may be an idiot

queen python Aug 2, 2019, 1:55 AM

#

The kids these days

#

Smh

upper karma Aug 2, 2019, 1:55 AM

#

They give you a perimeter

#

how old are you

queen python Aug 2, 2019, 1:55 AM

#

🤦

#

im 13

upper karma Aug 2, 2019, 1:55 AM

#

because you seem to lack online maturity

#

oh yep

queen python Aug 2, 2019, 1:55 AM

#

what's the perimeter

upper karma Aug 2, 2019, 1:56 AM

#

I can find it from there, thanks for the help

olive solar Aug 2, 2019, 1:56 AM

#

megathink

queen python Aug 2, 2019, 1:56 AM

#

np?

fossil ledge Aug 2, 2019, 1:56 AM

#

lol, it happens, just remember to read question carefully

queen python Aug 2, 2019, 1:56 AM

#

Yeah

fossil ledge Aug 2, 2019, 1:57 AM

#

most courses wont give misleading info until like senior year HS or uni really

queen python Aug 2, 2019, 1:57 AM

#

I don't think it's possible with that info

fossil ledge Aug 2, 2019, 1:57 AM

#

it is

tired laurel Aug 2, 2019, 1:57 AM

#

Since I’m taking geo soon, can someone tell me what I learn there

queen python Aug 2, 2019, 1:57 AM

#

Without perimeter

#

I didint know it's possible

#

?

upper karma Aug 2, 2019, 1:57 AM

#

@tired laurel a whole lot

olive solar Aug 2, 2019, 1:57 AM

#

~~geometry~~

fossil ledge Aug 2, 2019, 1:57 AM

#

you said with that info

upper karma Aug 2, 2019, 1:57 AM

#

shall I take a pic of a syllabus

fossil ledge Aug 2, 2019, 1:57 AM

#

oh send syllabus

tired laurel Aug 2, 2019, 1:57 AM

#

wOw

queen python Aug 2, 2019, 1:57 AM

#

i haven't taken geo

fossil ledge Aug 2, 2019, 1:57 AM

#

I love learning syllabuses

queen python Aug 2, 2019, 1:58 AM

#

It's just logic

fossil ledge Aug 2, 2019, 1:58 AM

#

helps me help others

upper karma Aug 2, 2019, 1:58 AM

#

🙃

queen python Aug 2, 2019, 1:58 AM

#

syllabuses?

upper karma Aug 2, 2019, 1:58 AM

#

dude if you don't know geo don't offer help

fossil ledge Aug 2, 2019, 1:58 AM

#

jfc you are one pretentious 13 yr old

queen python Aug 2, 2019, 1:58 AM

#

By I don't know it it means I didint take the course at school

tired laurel Aug 2, 2019, 1:58 AM

#

I mean

queen python Aug 2, 2019, 1:58 AM

#

I took it online

upper karma Aug 2, 2019, 1:58 AM

#

it's ok, keep going in life

#

a lot awaits you

tired laurel Aug 2, 2019, 1:58 AM

#

13 year olds don’t take it yet

queen python Aug 2, 2019, 1:59 AM

#

yes they do

tired laurel Aug 2, 2019, 1:59 AM

#

Pls stop flexing you’re making me feel bad

#

No freshmen year

queen python Aug 2, 2019, 1:59 AM

#

Im gonna take it in school this year

tired laurel Aug 2, 2019, 1:59 AM

#

14-15