#geometry-and-trigonometry

1 messages · Page 311 of 1

whole carbon
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yeah

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and 15

dark sparrow
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oh yeah there's an unfilled blank in 15

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okay so let's start with that then

whole carbon
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Okay

dark sparrow
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P(M & S)

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what percentage of the students like math and science?

whole carbon
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53?

dark sparrow
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why 53?

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where did you get 53 from

whole carbon
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I added both math and science percentages

dark sparrow
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did you add the 32 and the 21?

whole carbon
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yeah

dark sparrow
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32% is the percentage of people who like ONLY MATH
21% is the percentage of people who like ONLY SCIENCE

whole carbon
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Ohg

dark sparrow
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neither of these count towards the percentage of people liking BOTH MATH AND SCIENCE

whole carbon
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so 18?

dark sparrow
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there we go

whole carbon
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my fault

dark sparrow
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ok now let's move on to 16

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P(M & SS)

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what percentage of people like BOTH MATH AND SOCIAL STUDIES

whole carbon
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12

dark sparrow
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great

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P(M or SS or S)

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what percentage of people like math or science or social studies

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(i.e. at least one of the three)

whole carbon
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so any subject?

dark sparrow
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i said what i said

whole carbon
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oh

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okay so

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21

dark sparrow
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that... is way too low

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why 21?

whole carbon
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u said at least one of the three

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oh its 6

dark sparrow
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no

whole carbon
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what

dark sparrow
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i didn't say count the ones that like ALL THREE AT ONCE

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i said count the ones that like AT LEAST ONE THING

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first you counted only the ones who like just science

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then you counted only the ones who like all three at once

whole carbon
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im confused

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would it be 100

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lol

dark sparrow
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yes

whole carbon
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what does the U mean

dark sparrow
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union, which in this context is the same as or

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the upside down U is intersection, a.k.a. and

whole carbon
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so how do I do that one

dark sparrow
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P(M ∩ S ∩ SS) = the percentage of ppl who like math AND science AND socials

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i.e. all three at once

whole carbon
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oh

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Okay

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so 6

dark sparrow
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yes

whole carbon
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whats the U

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like wym by intersection or aka

dark sparrow
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a.k.a. means also known as

whole carbon
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yeah ik

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but how does that go in the math question

dark sparrow
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??

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ok fine

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∩ = AND

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∪ = OR

whole carbon
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so are they both 100?

dark sparrow
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no

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first one's 6 second one's 100

whole carbon
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but their both or

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ik

dark sparrow
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no they aren't!

whole carbon
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im talking about the other 100

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the one above it

dark sparrow
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oh

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yes then those are both the exact same thinhg

whole carbon
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ok

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okay so now 18

dark sparrow
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oh boy 18

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with the bad notation

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these should both be answered as "nonsensical" tbh

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cause you can't take the intersection of two numbers

whole carbon
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yeah its kinda confusing me

dark sparrow
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yeah let your teacher know their formatting and notation both suck

whole carbon
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lmfao

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so what is 18

dark sparrow
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i refuse to interpret bad notation as what's intended as opposed to what's written

whole carbon
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oh

stark plume
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Look at that document im sure i have aids

hybrid hornet
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sin(x) for all x in that interval is <0

silent plank
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the question is borked

dark sparrow
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the question is fucked up for exactly that reason @hybrid hornet

kindred walrus
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IM DEAD, I’ve never seen formatting like that for an assignment before 💀.

keen goblet
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Hey, im confused over one thing in trigonometry

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So in Quadrant 3

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Sin and cos are negative

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while tan is positive

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What im confused about is why is tan positive?

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actually i know why tan is positive, but why isnt the Sin and Cos positive?

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since the x and y axis are both negative in the 3rd quadrant

pure cape
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i think you just answered yourself, the sin and cos are negative in the 3rd quadrant

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because the axis consists of negative values in that area

keen goblet
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ye but -y/-x is positive

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i just realised the Hypotenuse is always positive, thats why they are negative in the 3rd quadrant

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problem solved

violet surge
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Hello everyone! I am an Italian student who will soon take an entrance test for the faculty of "Computer Engineering". Goniometry / trigonometry is my weak point. Do you have any material to help you learn more easily? Thanks so much in advance for the support

Problem solved

simple walrus
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anyone have any tools to easily study algebra 2/trig?

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i just need some good resources to rebuild and strengthen the basics of algebra

Problem solved nvm

empty granite
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Something to do with pythagoras theorem

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So so so so hard

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The measurements are correct but the diagram is not to scale

left zinc
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pls help

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these 2 shy

dark sparrow
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what's giving you trouble here?

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this is a matter of applying two things:

  • angles in a triangle add up to 180°
  • angles at the base of an isosceles triangle are the same
left zinc
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how to find x like this

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like whats the solving steps

silent plank
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this is a matter of applying two things:

  • angles in a triangle add up to 180°
  • angles at the base of an isosceles triangle are the same
dark sparrow
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^ that, and also i'm not a sir.

left zinc
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sorry.

dark sparrow
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just edit your message

left zinc
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omg i cant do

silent plank
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Q21: forget about the variables for a sec
can you determine the size of the base angles?

left zinc
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uh 64?

silent plank
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degress, yes

left zinc
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👀

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OMG

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X = 11

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y = 11

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TYYYY

upper karma
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@empty granite do you know the Pythagorean theorem?

empty granite
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Obviously

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@upper karma

upper karma
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Do you know how it’s applied?

empty granite
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I've solved it now but its much harder than it looks

upper karma
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Mhm well

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I would essentially just fill out enough data till there’s enough there to find the final length

pliant osprey
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i really liked bjshnog's solution. is that how y'all did it?

mental vessel
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i need help with this

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i know how to do the first part but b is where i get stuck

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its saying that the whole angle is 60 degrees

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but when i put it into a calculator it comes out to 66.4 degrees

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im just super confused

mental vessel
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?

upper karma
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It’s asking how far away the wire base attachment is from the base of the tower

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Just start fillin in data until you get what ya need

hollow raven
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@mental vessel
a)
You know the angle of elevation of the first rope is 60 deg, and the hypotenuse (length of the rope) is 10.0 m

How can we determine the ground distance?

Well we see that the ground is adjacent to the angle of elevation.

Angle, Adjacent Side, hypotenuse, how are these all related. Hold on, remember trig ratios?

SOH CAH TOA -> CAH -> cos(angle) = adj/hyp

cos(60) = adjacent/10.0 m
adjacent = cos(60)x10
adjacent = 0.5x10
adjacent side = 5.0 m

b)
Ok, now we know the adjacent side value, and we know that the second rope length (hypotenuse), is = 8.0 m.

Ok, try to figure this one out. How would you solve this? 🤔

mental vessel
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oh i got 4m

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instead of 5

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i used the 8 and cos60

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shouldnt it still be the same tho

hollow raven
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Well that can't be right, cause the second rope doesnt look like it has the same angle as the first rope

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so you have to find the angle using trig ratios again

mental vessel
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ill just show you my picture and you can pick it apart cause im pretty confused lol

hollow raven
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Hold on

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lemme give u another hint

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we know cos(angle) = adj/hyp

mental vessel
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yea

hollow raven
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We need to find the angle, and we have the adjacent side 5.0 m and hypotenuse 8.0 m

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so plugging those values in..

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you get cos(angle) = 5.0/8.0

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how would you isolate the angle in this case?

mental vessel
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ohhh

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yea okay

hollow raven
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hopefully you get the point

mental vessel
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i get how i got 4 instead of 5 because the inner angle isnt the same as the whole angle in the bigger triangle

hollow raven
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right

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the only thing that is similar about them is that their ground distance from the pole is equivalent

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Which is why you can reuse the adjacent side length from question (a) onto question (b)

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the best part is we didn't even need to use the pole height in this scenario!

mental vessel
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then you would subtract whatever 5/8 is off 60 to get the other angle right

hollow raven
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nope, you just need to isolate the angle from cos(angle) = 5.0/8.0 to get the angle measure

mental vessel
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oh

hollow raven
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cause the second rope creates a triangle of its own

mental vessel
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its asking for the triangle with the hypotenuse 8 right?

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angle

hollow raven
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Yep

mental vessel
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like its asking for the angle in the triangle with hypotenuse 8

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ohhh okay

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i thought it was asking for this anlge

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angle

hollow raven
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Nope, just the angle of elevation, which is the angle from the ground to the second wire

mental vessel
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ah okay

hollow raven
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hopefully i helped lol

mental vessel
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you did lol

hollow raven
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but yeah for any similar problems try looking at what you have and taking advantage of those trig ratios

mental vessel
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ill send my final product here in a lil bit to see if i did it correct cause this gets marked so haha

hollow raven
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sure

mental vessel
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yeah okay

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@hollow raven

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did I do it

hollow raven
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make sure to show step by step

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im not sure about c cause idk the question but b you got it

mental vessel
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Oh yeah sorry lol

hollow raven
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thats should be right

mental vessel
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Okay cool

hollow raven
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make sure to check over your work, cause you can't do a^2 + 5^2 = 8^2 then forget about a^2 in the next step

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and additionally
a = 2 + b
= a - b = 2
^ this is not needed

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but yeah u got the work down

mental vessel
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ahh okay

bronze jewel
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is anyone here good at geometry that can help me

next jackal
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bruh there are a lot of people here, just ask your question here and wait, if there's no one answering even after 15 mins, then ping helpers

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like "@ helpers " without space

nova rune
gaunt moon
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<@&286206848099549185> Idk if they answered or not yet but here ya go^^^^^

oak citrus
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@mental vessel bro get a tutor

upper karma
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@hollow raven next time don't just give them the answer right off the bat

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but nice solution

hollow raven
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oh yeah gotcha

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sort of new to the server ^_^

upper karma
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no problemo broother

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next time just start with step A and see if he can make it logically to step B

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so on and so fourth until he understands the problem

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he/she that is

hollow raven
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okay

upper karma
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👍

upper karma
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i wna do some geomegy problems lol

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geomegy looks cool

terse vine
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How is $(4 sec^2(\theta) - 4)^{(3/2)}$ equal to $4tan^2(\theta)^{(3/2)}$

somber coyoteBOT
terse vine
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I know the trig identity $cos^2(\theta) + sin^2(\theta) = 1$

somber coyoteBOT
terse vine
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So $(4 sec^2(\theta) - 4)^{(3/2)} = 4(sec^2(\theta) - 1)^{(3/2)} = 4(\frac{1}{cos^2(\theta)} - 1)^(3/2) = 4(\frac{cos^2\theta + sin^2\theta}{cos^2\theta} - 1)^{3/2} = 4(tan^2\theta - 1)^{3/2}$

somber coyoteBOT
terse vine
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How did they get rid of the -1 after $tan^2\theta$?

somber coyoteBOT
wind vector
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take lcm with -1

upper karma
wind vector
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(1-cosx ^2)/cosx ^2

upper karma
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I have no idea what process to take to solve this problem

wind vector
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why is 1/pi an odd one out in here

upper karma
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I don't know

wind vector
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lmao what is this problem

upper karma
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uni problem

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I mean I just don't know how to solve it 😦

wind vector
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me too

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we in the same boat

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OH WAIT

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they cut out a circle from the slice

terse vine
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But it's not exactly what solves your problem.

wind vector
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this is almost it

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but the thing is that it is a part of a circle not a triangle

somber coyoteBOT
wind vector
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all i know is that it has pi/3 radians

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angle

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why do i feel like it is 1/pi

terse vine
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Oh yeah you're right.

wind vector
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for no particular reason at all

terse vine
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Because it's about circles and the answer contains π in it? 🙃

wind vector
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yes

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the area of the piece of slice is pir^2/6

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what about the circle inscribed

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the answer is either 1/3 or 1/pi

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imo

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can't solve it lol

upper karma
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rip

wind vector
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also who parent gives his son a cutout from the bigger slice

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like ewhat

upper karma
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I mean I don't really want to know the answer

wind vector
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you are fooling your son

upper karma
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I want to know how to solve it

wind vector
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idk how to solve it lmao

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i failed

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the area of that slice is (pi*r^2)/6

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so that's that

fresh jasper
#

I know the eqn of a hyperbola.

The curve of two variables which are inversely proportional is also a hyperbola.

How can i show that 2 variable inversely proportional have a hyperbola curve using the eqn x^2/a^2 - y^2/b^2 = 1?

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Please tag me while answering

next flower
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hi could anyone help with a question im stuck on?

arctic vortex
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i will try to help you

upper karma
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Yes

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I have extensive knowledge of shapes

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Yep I know all the shapes

arctic vortex
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me too

upper karma
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Including yellow

arctic vortex
#

what

upper karma
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Ok @next flower ask questions

silent plank
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the only way to find out is to actually asked the math question

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asking to ask is pointless

arctic vortex
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ramonov hwo do i get the honorable role

upper karma
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by being honorable

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that’s how

next flower
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Okay so I did this how I usually do set them equal to find x but why does it matter if it is 60 ft long (Ik this might not seem hard)

arctic vortex
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how can i be honorable

upper karma
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That’s like asking for people to watch while you take initiative

arctic vortex
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being honorable?

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or asking to ask

upper karma
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Ok so

silent plank
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segment addition postulate

upper karma
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yea that’s

arctic vortex
#

i have to go to my homeroom class now

upper karma
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Yep

arctic vortex
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its 9:00 am

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bye guys

upper karma
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Ok

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Adios

next flower
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i did 4x+3=2x+21 did all the math and got 12

upper karma
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wrong

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They are not equal

silent plank
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why are you setting them equal?

next flower
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o

arctic vortex
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i thoguht u had to add them

upper karma
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bro

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Let him figure it out FeelsSpecialMan

arctic vortex
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sorry my A+ in geometry overall is leaking

upper karma
#

mmmk

silent plank
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the segments DO and OG form line DG, and you are told the length of that line

upper karma
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Well given you know the length of the line and they ask you to find 2 segments of unequal length that make up the line

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what to do?

next flower
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so i added them

upper karma
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mhm and

arctic vortex
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now i think its like algebra

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u have to do something

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but i cant asy it

upper karma
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No dip Sherlock

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He has to breathe

next flower
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6x+18

arctic vortex
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he is breahing

upper karma
#

Ok

arctic vortex
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===

upper karma
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That’s the two added

silent plank
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and the numerical value of that is:

arctic vortex
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now u have to do something with 60

next flower
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set that equal

arctic vortex
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yeaaaa

upper karma
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To what

arctic vortex
#

6x+10 ======= what

upper karma
#

+10

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Boi

arctic vortex
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oh it was 8

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oops

next flower
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6x+18=60

upper karma
#

Good

arctic vortex
#

yesss

upper karma
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Now solve

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For x

arctic vortex
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now what do u do

upper karma
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I mean x

arctic vortex
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i know what x is now

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its above 6 under 8

upper karma
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Can you don’t

next flower
#

7

upper karma
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Good

arctic vortex
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yess good job

next flower
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nice

upper karma
#

Now what’s the initial question?

next flower
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u guys are better than my teacher

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find x

arctic vortex
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and x is

upper karma
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Oh nvm that is the question

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Bababababam you found x good job

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100%

next flower
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thanks

upper karma
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yep

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Np

arctic vortex
#

100% but u required assistance so 80%

next flower
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it still says it wrong tho idk maybe its the site

arctic vortex
#

what

next flower
#

it says its wrong]

upper karma
#

6x + 18 = 60,
6x = 42
x = 7

arctic vortex
#

what

next flower
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and i went to the next problem which is find og

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and i got 35

upper karma
#

Maybe it wants you to give just the number

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Instead of the x =

next flower
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oh i did just do 7

upper karma
#

Ok maybe do x = 7

next flower
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it must be the way it was inputed by the teachers way

upper karma
next flower
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tried that to

upper karma
#

Weird

next flower
arctic vortex
#

what if we all are wrong

upper karma
#

Well plug them into each segment

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And tell me what they are

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25 + 35 = 60

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weird

arctic vortex
#

yea

upper karma
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Eh just move onto the next one

silent plank
#

just claim your marks from the work you show

next flower
arctic vortex
#

ramonov how old are u

next flower
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Those are the only ones I’ve been stuck on

silent plank
#

don't get hung up on crappy entry methods

arctic vortex
#

equal

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ab is equal to bc i think

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because b is the mindpoint

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so ab = bc

upper karma
#

Y e p

arctic vortex
#

yea

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u all seem like people who graduated

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everyone here is too smart

next flower
#

oh

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this website is pretty bad most of the time

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it says thats wrong to

arctic vortex
#

congruent

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then

next flower
#

yup

arctic vortex
#

yea

next flower
#

that was it

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also my teacher sucks

arctic vortex
#

mine too

next flower
#

she dosent really teach me

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just videos

arctic vortex
#

nice

next flower
#

no

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bad

upper karma
#

If i need to substract x+4 from 3x+2 would i do 3x+2-x+4 or 3x+2-x-4

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so second one

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alr

round prism
#

I need halllpppp pleaseee

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Oh nvm

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Actually I still need help

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How would I do this?

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Nvmmmm I just figured it out

next flower
#

i got a little into it

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got to 6x+11

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now im stuck

silent plank
#

howd you get that?

next flower
#

4x+10+2x-1

silent plank
#

does not give 6x+11

next flower
#

o

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lol

silent plank
#

also what's that supposed to be for

next flower
#

9

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meaning?

silent plank
#

6x-9 is :?

next flower
#

um

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well

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thats what im confused on

silent plank
#

why did you decide to add 4x+10 and 2x-1 together and how does that help you

next flower
#

idk

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thats why i need some help lol

obtuse tapir
#

4x+10+2x-1=9x-15

silent plank
#

adding them together gives you the length of the segment DF

next flower
#

yes then do that

silent plank
#

and you are also given the expression of in terms of x

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and using that you have an equation

obtuse tapir
#

the additions of all parts of a line gives the lenght of the whole tdboots

next flower
#

okay so just do the way you said greg

silent plank
#

solve for x, and hence determine the numerical value of DF = 9x-15

obtuse tapir
#

x=-4/-3

next flower
#

?

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two numbers

obtuse tapir
#

its a fraction

next flower
#

o

silent plank
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its incorrect though

next flower
#

i got x=8

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?

silent plank
#

yes

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good

next flower
#

then input

obtuse tapir
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oh wait

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i didnt add the brackets in

next flower
#

57?

obtuse tapir
#

calc error

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yep

silent plank
#

yes

next flower
#

yessss

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thank you

arctic vortex
#

oh wrong chanel

pale cargo
#

Hey wouldn't $cot^2(\theta) - sec^2(\theta) = 1$?

somber coyoteBOT
upper karma
#

Why do you think so?

pale cargo
#

Nvm It was csc - cot because of pythagorym identies

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identities

lunar junco
#

Can someone help me with this

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Would the answer be 3/5

runic pasture
#

what is sin a + sin b ?????

dark sparrow
#

you can simplify that to 2 sin( (a+b)/2 ) cos( (a-b)/2 )

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was that what you were looking for?

runic pasture
#

yes probably i don't really know, is there a way to demonstrate it just so i know

dark sparrow
#

...wait then what ARE you looking for

runic pasture
#

my question is : complete the formula sin a + sin b = .........
i'm preparing myself for an oral exam, it would be cool if i knew where it came from

dark sparrow
#

look up sum to product formulas

runic pasture
#

ok thanks

vale nimbus
#

i have to find the intersection point between the line DF and the plane AEGC

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i thought i'd project F onto EG and D onto AC then connect the projected points in the plane AEGC (and then the interscept of that line with the dotted line between DF would be the intersection point)

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sounds kinda sketchy + im not even too sure how i'd go about projecting

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would the projection of F be done perpendicular to EG and the projection of D perpendicular to AC?

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<@&286206848099549185>

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either that or just connecting EC and the intersection between EC and the dotted EF line would be the intersection point

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(these 2 ways end up giving me the same point but im still not sure weither or not this is correct + no correctoin key)

paper vale
#

you are not giving us enough information

vale nimbus
#

am i not?

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its a cut off pyramid

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thats about all im really told

paper vale
#

what do u mean find intersection

vale nimbus
#

just the point in which the line intersects with the plane

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like passes through it

paper vale
#

yea but what are the coordinates of these other points

vale nimbus
#

no coordinates

#

its not analytical

paper vale
#

but what do u mean find the point

vale nimbus
#

draw it

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like just mark it on the drawing where the point would be

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poor choice of words on my end there, true

paper vale
#

lol is that it?

vale nimbus
#

yes 🙂

paper vale
#

bruh

vale nimbus
#

soo did i get it or not

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i know its not a hard problem but as you can see im still confused

paper vale
#

i mean this is a 3d image on a 2d picture

#

u cant just mark the point like that lol

vale nimbus
#

yes you can

paper vale
#

actually the only way you could do it if it was some special point for example u know the ratios like being the midpoint and then u can just get a ruler

vale nimbus
#

Z is the the intersection point of PQ with the plane ADCB

paper vale
#

u cant just project it or wtv u were saying

vale nimbus
#

bro instead of get mad could you like help me? lmfao

paper vale
#

bruh

vale nimbus
#

to find the interscept of a line in a cube with the bottom plane of the cube u have to project

#

so yes you can do it with projecting

#

point P's projection is point Z

#

to find the intersception point of PQ with the plane ADCB

#

man i just want help 😭

#

@paper vale so are you gonna help or just keep proving me wrong

supple onyx
#

what's going on here?

vale nimbus
#

this message for the problem

#

can you help me?

paper vale
#

the locus of points which satisfy this condition is a perpendicular line to centre of square at bottom

supple onyx
#

as kane said, it does not seem as though there is enough information to do the problem

vale nimbus
#

i was just told what kind of figure it is

#

thats it

paper vale
#

so u know that it is gonna be directly above the centre of the bottom square pretty much

supple onyx
#

rectangle*

#

it's not specified as a regular pyramid

paper vale
#

yea i meant that

vale nimbus
#

this is the point what i get with my projection shit

#

idk if u can see it too well lol

paper vale
#

well find the midpoint of AC and draw vertical line

#

and its intersection with green is it

vale nimbus
#

yeah its the same point

#

lol

#

projection 🐐

#

now i have to find the intersception point between the line PQ and the plane EFGH

supple onyx
#

is this a cube?

vale nimbus
#

so i thought i'd just project P and Q onto the plane and then connect those points, then connect PQ and the intersception of the projected points' connection line and PQ would be the intersception point

#

yeah

supple onyx
#

or rectangular prism?

vale nimbus
#

its actually not stated

supple onyx
#

and how high above is P

vale nimbus
#

so a cube i guess?

supple onyx
#

these questions are pretty shit XD

vale nimbus
#

not specified either

#

now i have to find the intersception point between the line PQ and the plane EFGH
all thats said

supple onyx
#

is Q a midpoint?

paper vale
#

u cant work it out without knowing P's height

vale nimbus
#

nope

supple onyx
#

yeah exactly these questions are crap haha

vale nimbus
#

u just have to draw it

#

not find cords or know anything

#

just draw it

supple onyx
#

oh what

paper vale
#

well then draw it lol

supple onyx
#

then just kind of approximate with perspective

vale nimbus
#

well it has to be accurate :/

supple onyx
#

ruler from P to Q, and where it seems to be on EFGH by perspective

paper vale
#

yea u can literally just draw it and it is there

vale nimbus
#

but u have to find it accurately, not just guess

tribal wind
#

draw a line 🙂

vale nimbus
#

i think this is how its supposed to be done to find it accurately lol

tribal wind
#

looks good

vale nimbus
#

projection strat mocked yet again 😡

#

eh i hate these kinds of problems anyway

hollow raven
#

do we assume cube side length is n?

tribal wind
hollow raven
#

cross sections are very cool

paper vale
#

do we assume cube side length is n?
@hollow raven lol he isnt finding interesction, he is literally locating it

vale nimbus
#

i suck at cross sections

tribal wind
#

nah you're supposed to do like straightedge compass manipulations like transporting parallel lines and w/e

vale nimbus
#

kane seems mad that it isnt some big IQ question

#

pre-uni section bro calm down

paper vale
hollow raven
#

ok ok

#

that makes sense

vale nimbus
#

welp so i got both of them? lol

wheat swan
paper vale
#

you can use inverse tan to work out angles in two grey triangles

#

then subtract those from 90

fresh pike
#

where did the added 1's come from in the left and middle masures

#

in this one what is "borrowing" and why do you have to do it in the first place

hollow river
#

I'm taking geometry for 8th grade and a some others but I'm just wondering what algebra 1 skills I should brush up on

upper karma
#

question

#

inverse trig (i.e. tan^-1) is just used to find an angle

#

@ me

wheat swan
#

yeah i think so

#

thats what I used it for right now

#

@upper karma

#

@paper vale I did what you told me but I feel that I am wrong

#

<@&286206848099549185>

#

So I did the inverse of tan in the picture i sent earlier and I got approx. 4 for one and approx. 2 for the other one but that doesn't seem right to me

#

Would it just be 84?

#

Thats the picture of it

harsh lintel
#

The method should be right, not sure about the exact calcs cause I don’t have a calculator with me rn

#

It probably just seems weird cause the diagram isn’t to scale

wheat swan
#

Ok thank you I appreciate it

harsh lintel
#

Np

rocky rune
#

How do you find angles with only one side with SOH CAH TOA

dark sparrow
#

context?

#

one side alone is insufficient.

rocky rune
#

Never mind wrong calculations

real star
paper vale
#

do u know parallel line rules

real star
#

yes

paper vale
#

so u can set up an equation to get x

real star
#

dont they sum to 180?

paper vale
#

yea

#

so do 180-(one of them)=other one

real star
#

180-(x+60)

#

so 60-60 is 0

#

then 180-60 is 120

#

which leaves 120 and x

paper vale
#

u have made a mistake

real star
#

where

paper vale
#

well first u didnt do what i suggested

#

oh wait ur still on step 1, i thought that u claimed u solved nvm

#

ok so continue

real star
#

im confused

solid swan
#

just set (x+60) + (3x+10) = 180

real star
#

Because what I did was used the alternate interior angle theorem to find out the top angle of the isosceles triangle was 114 then I did 180-114 and got left with 66 and the base angles of a isosceles triangle are the same so 66/2 is 33

silent plank
#

alternate interior angle theorem
how exactly is that theorem relevant here

paper vale
#

yea all u need for this is opposite angles are equal and trianlge sum is 180

real star
#

how

silent plank
#

can you state the alternate interior angle theorem in its entirety

#

*(also angle sum on a line is 180°)

paper vale
#

ok so u know all the angles in the lower triangle

real star
#

yes

paper vale
#

therefore u know all angles in the triangle above it

real star
#

57, 66 and and 57

#

therefore u know all angles in the triangle above it
@paper vale how though

paper vale
#

do u know opposite angles thing

real star
#

yes

paper vale
#

well use that

real star
#

but its a whole triangle

#

im confused on how to do it

silent plank
#

don't see how it being a whole triangle makes a difference

#

determine what you know, write/mark it, and you have 1 less unknown to deal with

#

and then angle chase until you get what you want

paper vale
#

if u dont understand it, u can just use lines sum to 180 twice but there is no point

silent plank
#

which of a,b,c,d were you able to determine?

real star
#

a

#

a=57

#

and b=57 right?

silent plank
#

yes

real star
#

so 57+90=147

#

then 180-147=33

#

so c=33

#

and c and d are vertical angles so they are both 33

#

and 180-33=147

#

and base angles are the same so

#

147/2=x?

silent plank
#

yes

real star
#

so the reasoning is just vertical angles

#

and the sum of triangles are 180

silent plank
#

pretty much

jade heath
#

are there any unsolved/"open" problems in euclidean geometry ?

paper vale
#

Lol obviously there is

upper karma
jade heath
#

nice thanks

paper vale
#

It’s not that important but if u put < > around the link the big description thing doesn’t come up

upper karma
#

how would it look like

paper vale
#

It would just show the blue link

paper vale
#

But yea there are loads of open problems in every field, but not necessarily “important”

upper karma
#

ahaah dont worry

quartz prism
#

ok
see ya!

upper karma
#

good day

dusty sleet
#

hey

#

what does bgsin and Bgsin mean ?

paper vale
#

lol are u dutch

#

idk dutch, but i searched it up and it sent me to dutch wikipedia, and on that it said inverse sin

dusty sleet
#

so

#

yeah im dutch btw 🙂 but youre right

#

but im still wondering

#

is it just they give you for example

#

bgsin 1/2 and you will have to answer

#

pi/6 and 5pi/6

paper vale
#

well if they want the interval to be [0,2pi] then yea

#

but obviously as sin is periodic adding any multiple of 2pi to those also gives 1/2

iron rain
#

bgsin means boogsinus (arcsine)

paper vale
#

does boog mean arc in dutch

iron rain
#

yeah

dusty sleet
#

ohh thanks 🙂

paper vale
#

also u would need to consider negative values differently, but yea easy to work out

unborn bison
#

what do they want me to do here by finding PQ to nearest tenth? distance?

versed river
#

i assume so

upper karma
#

@unborn bison yes they want you to find the distance. and the midpoint.

#

of the line that connects them

blazing coyote
#

yo

#

can anyone help with this ^

silent plank
#

where are you stuck

blazing coyote
#

I'm not rly sure what to do first

#

im quite new to this concept haha

silent plank
#

whats the relation between angle 2 and 3

blazing coyote
#

vertical angles, right?

silent plank
#

yes

blazing coyote
#

ok

silent plank
#

you first two lines should look something like

somber coyoteBOT
blazing coyote
#

that makes sense thanks

#

but, where exactly do I go from there? showing that K and N are parallel

silent plank
#

what does that tell you about angles 1 and 3

blazing coyote
#

corresponding angles?

silent plank
#

uh, they're corresponding angles regardless of whether they're equal in size or the lines are parallel
what specifically do those first two lines tell you about angles 1 and 3

blazing coyote
#

erm... that they're parallel lines cut by a transversal?? sry im quite bad at this

silent plank
#

ignore the diagram

blazing coyote
#

vertical lines are congurent, so they're equal???

silent plank
#

what do <1 = <2
and <2 = <3
tell you about <1 and <3

fast radish
#

Hello

blazing coyote
#

that they're congruent?

fast radish
#

How do you remember the graphs of all of the trigonometric functions

silent plank
#

yes

fast radish
#

Especially the csc sec and cot

silent plank
#

equal things are equal, and that would be an application of the transitive property

#

$\angle1 \cong \angle3$ (transitive)

somber coyoteBOT
fast radish
#

Wha

#

I do simple trig not this stuff

silent plank
#

would be the next line in your 2col proof

fast radish
#

What even is transitive

blazing coyote
#

thanks man

#

that's it, that shows that the lines are parallel?

silent plank
#

you still need the conclusion

blazing coyote
#

ok

silent plank
#

k || n (converse of corresponding etc)

blazing coyote
#

So that concludes that these lines are parallel

#

thank you Ramonov

#

that concludes it?

silent plank
#

yes

blazing coyote
#

thank u

unborn bison
#

yeah midpoint was obvious, @upper karma, just didnt get distance

#

ty 😛

runic leaf
#

Can I ask who are good in calculus can I add you in the other discord? We need a tutor :))

upper karma
#

Are they coincident circles?

#

I am still trying to work out different arrangements of circles and see if I find an arrangement in which circles somehow coincide or something, but I can't fully grasp it

#

A small hint will be great

#

Np @unborn bison

dark sparrow
#

@upper karma the answer is that at least one person in the room is drunk, high, or otherwise lying

upper karma
#

lol, but seriously how do you work out the solution? I found the problem in Chapter Zero of Mathematical Circles, it can't be something trivial like a kids riddle or brain teaser (or maybe it can?)

silent plank
#

it can't be something trivial like a kids riddle or brain teaser
yes it is

#

its so bad

#

hint: on a sheet of paper as opposed to drawing on a whiteboard

upper karma
#

hint: on a sheet of paper as opposed to drawing on a whiteboard
@silent plank AHA

#

one can fold a sheet of paper

junior light
#

This problem is from Fomin, right?

upper karma
#

yes

junior light
#

Hmm, I didn't know the answer when I first read it but I learnt just now lol

#

I didn't even exactly understand that elephant passing through a hole in the paper problem(Ig a solution could be to tear the paper apart, but that isn't exactly a hole)

silent plank
#

what elephant problem

#

you don't even need to fold the paper

upper karma
#

ohk, I will work it out

slow void
vale nimbus
#

@slow void which one are you stuck on?

#

tbf i dont really like how there arent exact values given for the points that touch the x-axis lol

surreal bolt
#

Er so is it cosine or sine?

#

Then, what are A and C? (This deals with max, min y-values.)

#

Finally what is k? (This deals with period.)

grim cairn
dark sparrow
#

think about what functions have what signs in what quadrants

grim cairn
#

where would you find sec on a unit circle

mental vessel
#

how can i find the angles and the side lengths with only 2 values given, shouldnt it be at least 3? im confused

dark sparrow
#

@grim cairn think about what sec is defined as

upper karma
#

@mental vessel this channel is occupied, proceed with a free one.

grim cairn
#

hypotenuse / adjacent

#

@dark sparrow

dark sparrow
#

sec is 1/cos.

grim cairn
#

oops

#

yeah u rite

dark sparrow
#

sec has the same sign as cos

mental vessel
#

how can i find the angles and the side lengths with only 2 values given, shouldnt it be at least 3? im confused

earnest echo
#

Clearly it's an isoceles triangle

#

So if you know one angle you can find other two

paper mauve
#

just failed

#

it's fine

upper karma
#

@paper mauve was it a test

paper mauve
#

no a quiz

upper karma
#

Asking help on tests is not allowed here

paper mauve
silent plank
#

whats the difference between a test and a quiz

upper karma
#

Not sure but does not look something that respects academic honesty

upper karma
#

whats the difference between a test and a quiz
Good question

tribal wind
#

quizzes are when the exam tries to make you fail

keen lantern
#

How do i show that ABD is isosceles?

#

the only way i could think of is,

#

if angle ABC, and ACB are x

#

then BAD is 2x,

#

and ABD is 90 - x

#

making ADB 90 - x as well

#

but i feel like there's a much quicker and logical answer

bitter jetty
#

can i get helpp with this

upper karma
#

but i feel like there's a much quicker and logical answer
@keen lantern I found a neat solution

#

Just a moment

#

Rather than straight away giving the answer, I would like to know what you have tried so far for this question

#

Yes <BAD=2<x "<" here referring to "angle", and your other findings are also correct

#

making ADB 90 - x as well
but you haven't proved this lol

#

first you will need to prove that angle ABD=angle ADB

#

The main thing you need to do here, is to somehow relate angle ABD and angle ADB to angle x

#

||if you add both ABD and ADB you will get ext angle i.e. BAC, and BAC=180-2<x (angle sum property for triangle)||
||from here on you can substitute and eliminate to reach to the final conclusion that <ADB=<ABD||
||then you can use the property that sides opposite to equal angles in a triangle are equal||

#

try working on it yourself by using the hints above

#

I will send my sol. now

#

LP means linear pair and ASP means angle sum prop

#

Ah I made a mistake, instead of LP it should be complementary angles

silk patio
#

Draw a circle centred at A containing B and C. Because of the property of right angles in a circle, CD is the diameter. Hence AB = CD/2
As well as AD = AB like you wanted
@keen lantern
@upper karma

lapis stratus
#

http://puu.sh/Gv79a/75ad26be9b.png
hey guys, so I got this answer up until ((sin(x))(1-cos^2(x)))/cos^2(x) . I dont get where the 1-cos^2(x) comes from. I know sin = cos^2 - 1, but I dont understand what happens to the other cos^2(x) instead. If anyone can help that would be greatly appreciated : D
edited
Oh Nvm I just GOT IT!
I can just take out of the sinx's and then change it to distributive form Sin(x) (1 - cos(x))

upper karma
#

@silk patio Yes this is better

#

I haven't studied circles all that much yet so didn't think of that

#

Thanks

gritty sail
#

ew webassign lol

upper karma
#

Could anyone help me please, I don't really understand the question

deft cairn
#

5 of those equations will result in the graph on the right, one of them won't.

#

Remember where cos and sin start as well as your graph transformations, and you should be able to figure it out 👍

upper karma
#

okay thank youuu

delicate apex
tired terrace
#

@delicate apex do you still need help?

delicate apex
#

yes

tired terrace
#

Okay, so what its asking you to demonstrate a truth table with shading

#

Have you heard of a truth table?

#

(this also runs hand and hand with boolean algebra which you will probably look at later on)

upper karma
#

@delicate apex we ain’t gonna do this for you. What’s giving you trouble?

delicate apex
#

I dont understand any of it

upper karma
#

Is it homework?

#

Or is it a quiz or something?

mighty wharf
upper karma
tired terrace
upper karma
#

Cinnamónē

tired terrace
#

why am i smooth brain

upper karma
mighty wharf
upper karma
tired terrace
upper karma
mighty wharf
upper karma
tired terrace
mighty wharf
upper karma
#

P 👀

mighty wharf
#

We should prolly stop

upper karma
#

Pfft

#

Seriously though

tired terrace
#

ya

upper karma
#

It is not nice to leave the chat after answering a question

#

Er

#

Asking one

tired terrace
#

right wasnt there a question?

mighty wharf
#

No reply

upper karma
#

There was at one point but I think he expects us to do it for him... either that or he just needed to go

#

And image is messy cuz of that ‘exit’ thing

#

Anyways

#

Why is this in geo-trig?

mighty wharf
junior light
#

Why is this in geo-trig?
Apparently some people think Venn Diagrams are about circles and rectangles.

ashen rain
#

Lmao

vale lintel
#

||tbbt||

nocturne thicket
#

am i stupid

#

this is just 60 right

#

or am i just dumb

earnest echo
#

No, it's not 60

nocturne thicket
#

OH its 30

#

@earnest echo right?

earnest echo
#

Yeah

nocturne thicket
#

ah i see

#

i was like wtf theres no way its that simple

#

im guessing i got this one wrong too?

earnest echo
#

Looks alright to me

nocturne thicket
#

alright ty

#

i just did 14.9*6

earnest echo
#

👍

upper karma
#

like i legitimately dont understand wtf just happened

#

why does the cosine rule have that many numbers on it ;v;

mighty wharf
#

Do you know the cosine formula

upper karma
#

yes i know

#

but wouldnt it just be

mighty wharf
#

a²=b²+c²-2bc CosA

upper karma
#

if theyre doing cosine c it would just be (50/71) would it not ;v; why was there all square routes doe

#

O H

#

I THOUGHT

#

IT WAS

#

omg

#

i am braindead

mighty wharf
#

no lol

#

not that cos rule

upper karma
#

thank u ;v;

mighty wharf
#

no problem

upper karma
#

right um could you elaborate a bit further on why it's a fraction doe ;v;

mighty wharf
#

just solve everything in the bracket

#

then find the cos inverse

#

arccos

#

,calc 50^2+71^2-50^2

somber coyoteBOT
#

Result:

5041
mighty wharf
#

,calc 25071

somber coyoteBOT
#

Result:

7100
upper karma
#

im really confused on why they used those numbers though ;v;

#

like

#

i thought the formula was

mighty wharf
#

,calc 5041/7100

somber coyoteBOT
#

Result:

0.71
upper karma
mighty wharf
#

so arccos of 0.71 gives you your C°

#

nooo

#

I mean yeah

upper karma
#

like why they b didin

#

dividin

#

sorry im like

#

pea brain

mighty wharf
#

but that's the same thing as $c²=a²+b²-2abcosC$

somber coyoteBOT
mighty wharf
#

let me explain

#

you know the rule is $c²=a²+b²-2abcosC$

somber coyoteBOT
mighty wharf
#

but in this case

#

you have c²

upper karma
#

right

mighty wharf
#

and you don't have cosC

#

so you want to surrogate them

#

so you can find your cosC

paper vale
#

it is trivial

upper karma
#

so you wanna replace the c2 w the cosC

#

thats why the equation changed?

mighty wharf
#

yes

#

so you divide both sides

upper karma
#

aH

#

tHATS HW

#

i'm legitimately pea brained

#

thank you sm

mighty wharf
#

do you get it though

upper karma
#

yes

mighty wharf
#

divide both sides by -2bcCosC

upper karma
#

they were using that equation but just modifying it so it could be cosC = right

#

mhm

#

also um do you mind if i send a friend req so i can ask more pea brained questions sometimes pls ;v;

mighty wharf
#

no problem

#

but I'm going somewhere rn

#

you can always ask anyone though, maybe they even can explain better

upper karma
#

ah yea thats fine

paper vale
#

the best thing to do is to try and work it out yourself

upper karma
#

thank you so much for the clear explanation though

#

ah okay

#

will do c: thank you for your help

mighty wharf
#

np

upper karma
#

i just found this

#

holy shit i AM pea brained

mighty wharf
#

You were supposed to be taught that before given that kind of question

upper karma
#

unfortunately my math teacher is a terrible communicator

#

we're given assignments before class ;v;

#

im doing ibd and hahhah im fucked probs

mighty wharf
#

Bye for now.

upper karma
#

cya o:

#

um how do i write this on a tinspire

#

;v;

#

i tried nsolve but it wouldn't work

paper vale
#

try clicking the correct buttons