#geometry-and-trigonometry
1 messages · Page 311 of 1
Okay
53?
I added both math and science percentages
did you add the 32 and the 21?
yeah
32% is the percentage of people who like ONLY MATH
21% is the percentage of people who like ONLY SCIENCE
Ohg
neither of these count towards the percentage of people liking BOTH MATH AND SCIENCE
so 18?
there we go
my fault
ok now let's move on to 16
P(M & SS)
what percentage of people like BOTH MATH AND SOCIAL STUDIES
12
great
P(M or SS or S)
what percentage of people like math or science or social studies
(i.e. at least one of the three)
so any subject?
i said what i said
no
what
i didn't say count the ones that like ALL THREE AT ONCE
i said count the ones that like AT LEAST ONE THING
first you counted only the ones who like just science
then you counted only the ones who like all three at once
yes
what does the U mean
union, which in this context is the same as or
the upside down U is intersection, a.k.a. and
so how do I do that one
P(M ∩ S ∩ SS) = the percentage of ppl who like math AND science AND socials
i.e. all three at once
yes
a.k.a. means also known as
so are they both 100?
no they aren't!
oh boy 18
with the bad notation
these should both be answered as "nonsensical" tbh
cause you can't take the intersection of two numbers
yeah its kinda confusing me
yeah let your teacher know their formatting and notation both suck
i refuse to interpret bad notation as what's intended as opposed to what's written
oh
Look at that document im sure i have aids
am i tweaking or does x not have a solution
sin(x) for all x in that interval is <0

the question is borked
the question is fucked up for exactly that reason @hybrid hornet
IM DEAD, I’ve never seen formatting like that for an assignment before 💀.
Hey, im confused over one thing in trigonometry
So in Quadrant 3
Sin and cos are negative
while tan is positive
What im confused about is why is tan positive?
actually i know why tan is positive, but why isnt the Sin and Cos positive?
since the x and y axis are both negative in the 3rd quadrant
i think you just answered yourself, the sin and cos are negative in the 3rd quadrant
because the axis consists of negative values in that area
ye but -y/-x is positive
i just realised the Hypotenuse is always positive, thats why they are negative in the 3rd quadrant
problem solved
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
anyone have any tools to easily study algebra 2/trig?
i just need some good resources to rebuild and strengthen the basics of algebra
Problem solved nvm
Something to do with pythagoras theorem
So so so so hard
The measurements are correct but the diagram is not to scale
what's giving you trouble here?
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
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
^ that, and also i'm not a sir.
sorry.
just edit your message
omg i cant do
Q21: forget about the variables for a sec
can you determine the size of the base angles?
uh 64?
degress, yes
@empty granite do you know the Pythagorean theorem?
Do you know how it’s applied?
I've solved it now but its much harder than it looks
Mhm well
I would essentially just fill out enough data till there’s enough there to find the final length
i really liked bjshnog's solution. is that how y'all did it?
i need help with this
i know how to do the first part but b is where i get stuck
its saying that the whole angle is 60 degrees
but when i put it into a calculator it comes out to 66.4 degrees
im just super confused
?
It’s asking how far away the wire base attachment is from the base of the tower
Just start fillin in data until you get what ya need
@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? 🤔
oh i got 4m
instead of 5
i used the 8 and cos60
shouldnt it still be the same tho
Well that can't be right, cause the second rope doesnt look like it has the same angle as the first rope
so you have to find the angle using trig ratios again
ill just show you my picture and you can pick it apart cause im pretty confused lol
yea
We need to find the angle, and we have the adjacent side 5.0 m and hypotenuse 8.0 m
so plugging those values in..
you get cos(angle) = 5.0/8.0
how would you isolate the angle in this case?
hopefully you get the point
i get how i got 4 instead of 5 because the inner angle isnt the same as the whole angle in the bigger triangle
right
the only thing that is similar about them is that their ground distance from the pole is equivalent
Which is why you can reuse the adjacent side length from question (a) onto question (b)
the best part is we didn't even need to use the pole height in this scenario!
then you would subtract whatever 5/8 is off 60 to get the other angle right
nope, you just need to isolate the angle from cos(angle) = 5.0/8.0 to get the angle measure
oh
cause the second rope creates a triangle of its own
Yep
like its asking for the angle in the triangle with hypotenuse 8
ohhh okay
i thought it was asking for this anlge
angle
Nope, just the angle of elevation, which is the angle from the ground to the second wire
ah okay
hopefully i helped lol
you did lol
but yeah for any similar problems try looking at what you have and taking advantage of those trig ratios
ill send my final product here in a lil bit to see if i did it correct cause this gets marked so haha
sure
make sure to show step by step
im not sure about c cause idk the question but b you got it
thats should be right
Okay cool
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
and additionally
a = 2 + b
= a - b = 2
^ this is not needed
but yeah u got the work down
ahh okay
is anyone here good at geometry that can help me
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
like "@ helpers " without space
how do i do this
<@&286206848099549185> Idk if they answered or not yet but here ya go^^^^^
@mental vessel bro get a tutor
@hollow raven next time don't just give them the answer right off the bat
but nice solution
no problemo broother
next time just start with step A and see if he can make it logically to step B
so on and so fourth until he understands the problem
he/she that is
okay
👍
Xhendos:
I know the trig identity $cos^2(\theta) + sin^2(\theta) = 1$
Xhendos:
So $(4 sec^2(\theta) - 4)^{(3/2)} = 4(sec^2(\theta) - 1)^{(3/2)} = 4(\frac{1}{cos^2(\theta)} - 1)^(3/2) = 4(\frac{cos^2\theta + sin^2\theta}{cos^2\theta} - 1)^{3/2} = 4(tan^2\theta - 1)^{3/2}$
Xhendos:
How did they get rid of the -1 after $tan^2\theta$?
Xhendos:
take lcm with -1
(1-cosx ^2)/cosx ^2
I have no idea what process to take to solve this problem
why is 1/pi an odd one out in here
I don't know
lmao what is this problem
I thought I've seen your problem on MindYourDecision his YouTube channel.
https://www.youtube.com/watch?v=9HH6D5oM9hc
High school geometry is the only super power you need to solve this puzzle!
Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1
Send me suggestions by email (address in video). I consider all ideas though can't always reply!
Like many YouTubers I us...
But it's not exactly what solves your problem.
Xhendos:
Oh yeah you're right.
for no particular reason at all
Because it's about circles and the answer contains π in it? 🙃
yes
the area of the piece of slice is pir^2/6
what about the circle inscribed
the answer is either 1/3 or 1/pi
imo
can't solve it lol
rip
I mean I don't really want to know the answer
you are fooling your son
I want to know how to solve it
idk how to solve it lmao
i failed
the area of that slice is (pi*r^2)/6
so that's that
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?
Please tag me while answering
hi could anyone help with a question im stuck on?
i will try to help you
me too
what
Ok @next flower ask questions
the only way to find out is to actually asked the math question
asking to ask is pointless
ramonov hwo do i get the honorable role
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)
how can i be honorable
That’s like asking for people to watch while you take initiative
Ok so
segment addition postulate
yea that’s
i have to go to my homeroom class now
Yep
i did 4x+3=2x+21 did all the math and got 12
why are you setting them equal?
o
i thoguht u had to add them
sorry my A+ in geometry overall is leaking
mmmk
the segments DO and OG form line DG, and you are told the length of that line
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
what to do?
so i added them
mhm and
6x+18
he is breahing
Ok
===
That’s the two added
and the numerical value of that is:
now u have to do something with 60
set that equal
yeaaaa
To what
6x+10 ======= what
6x+18=60
Good
yesss
now what do u do
I mean x
Can you don’t
7
Good
yess good job
nice
Now what’s the initial question?
and x is
thanks
100% but u required assistance so 80%
it still says it wrong tho idk maybe its the site
what
it says its wrong]
6x + 18 = 60,
6x = 42
x = 7
what
oh i did just do 7
Ok maybe do x = 7
it must be the way it was inputed by the teachers way

tried that to
Weird

what if we all are wrong
yea
Eh just move onto the next one
just claim your marks from the work you show
Also what could this be
ramonov how old are u
Those are the only ones I’ve been stuck on
don't get hung up on crappy entry methods
Y e p
yup
yea
mine too
nice
If i need to substract x+4 from 3x+2 would i do 3x+2-x+4 or 3x+2-x-4

so second one
alr
I need halllpppp pleaseee
Oh nvm
Actually I still need help
How would I do this?
Nvmmmm I just figured it out
howd you get that?
4x+10+2x-1
does not give 6x+11
also what's that supposed to be for
6x-9 is :?
why did you decide to add 4x+10 and 2x-1 together and how does that help you
4x+10+2x-1=9x-15
adding them together gives you the length of the segment DF
yes then do that
and you are also given the expression of in terms of x
and using that you have an equation
the additions of all parts of a line gives the lenght of the whole tdboots
okay so just do the way you said greg
solve for x, and hence determine the numerical value of DF = 9x-15
x=-4/-3
its a fraction
o
its incorrect though
then input
57?
yes
Hey wouldn't $cot^2(\theta) - sec^2(\theta) = 1$?
Albot1288:
Why do you think so?
what is sin a + sin b ?????
you can simplify that to 2 sin( (a+b)/2 ) cos( (a-b)/2 )
was that what you were looking for?
yes probably i don't really know, is there a way to demonstrate it just so i know
...wait then what ARE you looking for
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
look up sum to product formulas
ok thanks
i have to find the intersection point between the line DF and the plane AEGC
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)
sounds kinda sketchy + im not even too sure how i'd go about projecting
would the projection of F be done perpendicular to EG and the projection of D perpendicular to AC?
<@&286206848099549185>
either that or just connecting EC and the intersection between EC and the dotted EF line would be the intersection point
(these 2 ways end up giving me the same point but im still not sure weither or not this is correct + no correctoin key)
you are not giving us enough information
what do u mean find intersection
yea but what are the coordinates of these other points
but what do u mean find the point
draw it
like just mark it on the drawing where the point would be
poor choice of words on my end there, true
lol is that it?
yes 🙂
bruh
soo did i get it or not
i know its not a hard problem but as you can see im still confused
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
Z is the the intersection point of PQ with the plane ADCB
u cant just project it or wtv u were saying
bro instead of get mad could you like help me? lmfao
bruh
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
what's going on here?
the locus of points which satisfy this condition is a perpendicular line to centre of square at bottom
as kane said, it does not seem as though there is enough information to do the problem
so u know that it is gonna be directly above the centre of the bottom square pretty much
yea i meant that
this is the point what i get with my projection shit
idk if u can see it too well lol
well find the midpoint of AC and draw vertical line
and its intersection with green is it
yeah its the same point
lol
projection 🐐
now i have to find the intersception point between the line PQ and the plane EFGH
is this a cube?
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
or rectangular prism?
its actually not stated
and how high above is P
so a cube i guess?
these questions are pretty shit XD
not specified either

now i have to find the intersception point between the line PQ and the plane EFGH
all thats said
is Q a midpoint?
u cant work it out without knowing P's height
nope
yeah exactly these questions are crap haha
oh what
well then draw it lol
then just kind of approximate with perspective
ruler from P to Q, and where it seems to be on EFGH by perspective
yea u can literally just draw it and it is there
but u have to find it accurately, not just guess
draw a line 🙂
looks good
do we assume cube side length is n?
it's more fun when it's a game https://play.google.com/store/apps/details?id=com.hil_hk.xsection&hl=en_US
cross sections are very cool
do we assume cube side length is n?
@hollow raven lol he isnt finding interesction, he is literally locating it
i suck at cross sections
nah you're supposed to do like straightedge compass manipulations like transporting parallel lines and w/e

welp so i got both of them? lol
Can anyone help me get started on this?
you can use inverse tan to work out angles in two grey triangles
then subtract those from 90
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
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
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
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
Ok thank you I appreciate it
Np
How do you find angles with only one side with SOH CAH TOA
Never mind wrong calculations
I need to find the value of x but I'm not sure where to start
do u know parallel line rules
yes
so u can set up an equation to get x
dont they sum to 180?
u have made a mistake
where
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
im confused
just set (x+60) + (3x+10) = 180
X would be 33 here right?
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
alternate interior angle theorem
how exactly is that theorem relevant here
yea all u need for this is opposite angles are equal and trianlge sum is 180
how
can you state the alternate interior angle theorem in its entirety
*(also angle sum on a line is 180°)
ok so u know all the angles in the lower triangle
yes
therefore u know all angles in the triangle above it
57, 66 and and 57
therefore u know all angles in the triangle above it
@paper vale how though
do u know opposite angles thing
yes
well use that
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
if u dont understand it, u can just use lines sum to 180 twice but there is no point
yes
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?
yes
pretty much
are there any unsolved/"open" problems in euclidean geometry ?
Lol obviously there is
nice thanks
It’s not that important but if u put < > around the link the big description thing doesn’t come up
how would it look like
It would just show the blue link
But yea there are loads of open problems in every field, but not necessarily “important”
ahaah dont worry
ok
see ya!
good day
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
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
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
bgsin means boogsinus (arcsine)
does boog mean arc in dutch
yeah
ohh thanks 🙂
also u would need to consider negative values differently, but yea easy to work out
i assume so
@unborn bison yes they want you to find the distance. and the midpoint.
of the line that connects them
where are you stuck
whats the relation between angle 2 and 3
vertical angles, right?
yes
ok
you first two lines should look something like
ramonov:
that makes sense thanks
but, where exactly do I go from there? showing that K and N are parallel
what does that tell you about angles 1 and 3
corresponding angles?
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
erm... that they're parallel lines cut by a transversal?? sry im quite bad at this
ignore the diagram
vertical lines are congurent, so they're equal???
what do <1 = <2
and <2 = <3
tell you about <1 and <3
Hello
that they're congruent?
How do you remember the graphs of all of the trigonometric functions
yes
Especially the csc sec and cot
equal things are equal, and that would be an application of the transitive property
$\angle1 \cong \angle3$ (transitive)
ramonov:
would be the next line in your 2col proof
What even is transitive
you still need the conclusion
ok
k || n (converse of corresponding etc)
So that concludes that these lines are parallel
thank you Ramonov
that concludes it?
yes
thank u
Can I ask who are good in calculus can I add you in the other discord? We need a tutor :))
I CAN'T FIGURE OUT THIS PUZZLE PLEASE HELP I AM GOING INSANE
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
Perhaps something like this? Or maybe I am just overthinking and they are simply coincident circles
@upper karma the answer is that at least one person in the room is drunk, high, or otherwise lying
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?)
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

hint: on a sheet of paper as opposed to drawing on a whiteboard
@silent plank AHA
one can fold a sheet of paper
This problem is from Fomin, right?
yes
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)
ohk, I will work it out
@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
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.)
any idea of what to do here
think about what functions have what signs in what quadrants
where would you find sec on a unit circle
how can i find the angles and the side lengths with only 2 values given, shouldnt it be at least 3? im confused
@grim cairn think about what sec is defined as
@mental vessel this channel is occupied, proceed with a free one.
sec is 1/cos.
sec has the same sign as cos
how can i find the angles and the side lengths with only 2 values given, shouldnt it be at least 3? im confused
@paper mauve was it a test
no a quiz
Asking help on tests is not allowed here

whats the difference between a test and a quiz
Not sure but does not look something that respects academic honesty
whats the difference between a test and a quiz
Good question
quizzes are when the exam tries to make you fail
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
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
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
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))
@silk patio Yes this is better
I haven't studied circles all that much yet so didn't think of that
Thanks
ew webassign lol
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 👍
okay thank youuu
can anyone help
@delicate apex do you still need help?
yes
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)
@delicate apex we ain’t gonna do this for you. What’s giving you trouble?
I dont understand any of it



why am i smooth brain









P 👀
We should prolly stop
ya
right wasnt there a question?
No reply
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?

Why is this in geo-trig?
Apparently some people think Venn Diagrams are about circles and rectangles.
Lmao
||tbbt||
No, it's not 60
Yeah
ah i see
i was like wtf theres no way its that simple
im guessing i got this one wrong too?
Looks alright to me
👍
could someone explain this section to me?
like i legitimately dont understand wtf just happened
why does the cosine rule have that many numbers on it ;v;
Do you know the cosine formula
a²=b²+c²-2bc CosA
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
thank u ;v;
no problem
right um could you elaborate a bit further on why it's a fraction doe ;v;
just solve everything in the bracket
then find the cos inverse
arccos
,calc 50^2+71^2-50^2
Result:
5041
,calc 25071
Result:
7100
im really confused on why they used those numbers though ;v;
like
i thought the formula was
,calc 5041/7100
Result:
0.71
but that's the same thing as $c²=a²+b²-2abcosC$
raelo:
raelo:
right
it is trivial
do you get it though
yes
divide both sides by -2bcCosC
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;
no problem
but I'm going somewhere rn
you can always ask anyone though, maybe they even can explain better
ah yea thats fine
the best thing to do is to try and work it out yourself
thank you so much for the clear explanation though
ah okay
will do c: thank you for your help
np
You were supposed to be taught that before given that kind of question
unfortunately my math teacher is a terrible communicator
we're given assignments before class ;v;
im doing ibd and hahhah im fucked probs
Bye for now.
cya o:
um how do i write this on a tinspire
;v;
i tried nsolve but it wouldn't work
try clicking the correct buttons


