geometry-and-trigonometry

[nocturne remnant]

Why would the “interior angles” of a circle sum to 360 degrees? You’re talking about something totally different here.

[fiery oriole]

this question’s always bothered me for the longest time possible; why would a square of 1 metre length have an area of 1 square metre?

couldn’t it be 100 metres if you convert to cm first, and then convert back to metres?

[pliant basin]

hows the thing that separates the base of a triangle into two equal sizes called

like theres the height, angle bisector and the other thing

[nocturne remnant]

One metre is one hundred centimetres, and one square metre is one hundred hundred (i.e. 10000) square centimetres.

[lost marlin]

because you also square the unit. 1 metre X 1 metre = 1 square metre. 100 metre X 100 metre = 10.000 square metre

[lost marlin]

idk if in english you really call it by this name, but the translator says median. In portuguese is “Mediana” btw

[dark sparrow]

that's the definition of a square meter, and 100 cm^2 don't make 1 m^2 as stated above

[wind coral]

<@&268886789983436800>

[rustic yew]

guys how do u solve this

im confused

A helicopter is being used to move a large pipe from a circular cut-out of rock face high up on a cliff. The helicopter drops two ropes that are attached to pipe ends. Given that a=84 feet, b=97 feet, and c=43 feet, what is the length of x? (Round your answer to one decimal place, if necessary.

I legit dont understand how to do

[spark stag]

is that all you know?

as that does not seem like sufficient data

oh, duh, its in a circle

[grave pond]

Power of a point poblem.

[spark stag]

yep

somehow i missed the "circular" entirely (i'll blame it on the image not being a perfect circle)

[grave pond]

Gotta love practical application problems.

[spark stag]

in any case, here's the relevant statement

so if we call the helicopter's point "h", we have ha * hx = hb * hc

since hx (the distance from h to x) is the entire length of a + x, and similar for hc, this becomes... [do this yourself]

solve for x.

[worthy latch]

ive literally seen the same problem on a geometry test i took before lol

[rustic yew]

lol

[ripe echo]

How would I solve this?

[grave pond]

Law of cosines.

[warped bone]

Yup

[sweet linden]

For this half angle calculation, why is pi/4 placed where cos is? I thought cos was supposed to denote the x value, so why would you use the y value instead?

[silent plank]

theta is the angle being halved

tan(theta/2) = ...

[warped bone]

Are we talking about the half angle formula?

[sweet linden]

Yes

[sweet linden]

pi/4 divided by 2

But I'm not sure why that means its cosine theta

Oh wait

So tan of pi/4 divided by two would be 2 divided by pi/4?

And then pi/4 would be in the denominator, thus cos?

[silent plank]

$\tan\br{\frac{\theta}{2}}= \overset{?}{\pm} \sqrt{\frac{1- \cos(\theta)}{1+\cos(\theta)}}$

[somber coyote]

ℝamonov

[sweet linden]

Yes I know the formula

But I still don't get how that translates if my inference is wrong

[silent plank]

pi/8 expressed in the form
something divided by 2 is
(pi/4)/2

and comparing that to
theta/2,

theta is pi/4

[sweet linden]

So you're just placing theta wherever it is in the formula then

[silent plank]

yes

[sweet linden]

Idk why that was so confusing for me

Anyways thanks that makes sense now

Guess I was overthinking it

[marble smelt]

I'm not sure how dumb this question is, but I was given this problem without enough information (to my knowledge.) I don't know if I should do what they might want me to do by assuming ABC is 90 and then showing that I understand it, or if I'm supposed to say this is wrong. I'm not able to contact the teacher, now and the future. This is more of a social question. What would you do, and what should I do?? (B specifically)

[nocturne remnant]

Probably assume ABC is 90

Actually idk

[marble smelt]

I've searched this question online and I see slightly more people saying there isn't enough information than the answer assuming ABC is 90

[lost marlin]

Idk if the text under the question is your answer or not, but it’s totally correct

100% correct

[marble smelt]

it is my answer

[lost marlin]

Anything different from that is based on assumptions, which is wrong

[lost marlin]

Congrats Dankulus. A lot of people would just assume that the image contains a 90° angle

[upper karma]

4 sin x cos x + 2 sin x + 2 cos x +1 =0

[upper karma]

what s the general solution

<@&286206848099549185>

[snow crystal]

Try grouping the terms

[upper karma]

( pi/6+kpi -pi/3+kpi)is it right?

[snow crystal]

Uhh no

i'll give you the explanation in like an hour unfortunately cuz I can't use my phone rn

[upper karma]

ok thanks

[weary hound]

Hint: 4sinxcosx+2sinx+2cosx+1= (2cosx+1)(2sinx+1)=0

ab=0 directry translates to a=0 or b=0

[upper karma]

can someone help me

[upper karma]

is number9 y+5=2y

what do i write for the x part?

[snow crystal]

,rotate

[snow crystal]

I know that my handwriting isn't the best so ask if something's not clear

[upper karma]

can someone help me with this

[warm bramble]

So since the lines are parallel the need to total 180 so x+100=180 so x=80
That's the explanation in a nutshell but yeah

[upper karma]

ahhh

did i do the y part correct

[warm bramble]

Yea

You got y=5 right?

[upper karma]

what about number 10

[upper karma]

yep

[upper karma]

is it x+14=3x+2

[warm bramble]

For number 10 you have that all angles are right so it's a rectangle so you know that the lines which are parallel are equal
So for x you have
x+14=3x+2
And so, what do you have for y?

[upper karma]

2y+1=4y-5

[upper karma]

number 9 is a parallelogram right?

[warm bramble]

Yea exactly, for both of what you said

[upper karma]

so 9 and 10 are both paralelograms

[warm bramble]

Overall yeah but 10 is a more specific parallelogram

[upper karma]

what kind?

[warm bramble]

A rectangle
Parallelograms is a general term which has subsections
Rectangles (img 1) which is the shape on number 10 since all of its angles are right angles
Rhombus (img 2) which isn't really that important (Come to think of it number 9 is a rhombus cause it all of its sides are equal without having any right angles)
And lastly a square (img 3) which is a combination of a rectangle and a rhombus, meaning all of its angles are right angles and all of its sides are equal

This is a very detailed explanation sorry, I do think it can come in handy though

[upper karma]

yea im saving it lol

@warm bramble can u help me with 2 more problems??

[warm bramble]

Yeah sure

[upper karma]

these 2

[upper karma]

thanks

[lapis torrent]

For number 1, the ans is 120 deg and the second one is 69 deg

[upper karma]

how did u get it

[lapis torrent]

Using that the sum of two co interior angles is equal to 180 deg

[lapis torrent]

If u dont get it, theb dm me i will explain it

N*

[upper karma]

okay

i dmed

[upper karma]

ahh

[wary scarab]

I didn't knew that, i just knew this other

[wary scarab]

Do you know the name of this other?

@whole venture ?

[whole venture]

It's called the consecutive interior angles theorem.

[wary scarab]

A teacher told me about that, but he doesn't told me the name

@whole venture thank you so much.

[upper karma]

thanks i didnt know this

[upper karma]

thanks alot

[upper karma]

how do we do this

do we do number 13 by doing 8+14/2?

so its gonna 22/2 so then its 11

right?

[snow crystal]

yeah

[upper karma]

and for 14 is it 25+15/2

[snow crystal]

exactly

[upper karma]

and thats all i do right?

[snow crystal]

yup

[upper karma]

how do i do 16?

[snow crystal]

what's m K

angle K?

[upper karma]

yes

idk how to do 16

[snow crystal]

if it's a kite then angle M= angle K

[upper karma]

yea idk how to find angle M

[snow crystal]

what's the sum of all angles in a quadrangle

[upper karma]

do i do 110+80?

[snow crystal]

this is what you have now

you have to figure out what I asked

I assumed that you know that, it's elementary knowledge

[upper karma]

ye

[snow crystal]

(n-2) * 180 degrees, this is the formula for the sum of angles in polygon

where n is the number of sides

[upper karma]

4

Wait

(4-2)x180?

isnt that 360

[snow crystal]

it is

[upper karma]

yea

[snow crystal]

what do you do next

[upper karma]

find angle M

[snow crystal]

if you have something like this

and you know that 80°+110°+x+x=360°

what do you do

[upper karma]

190+2x=360

2x=170

x=85

[snow crystal]

congrats

[upper karma]

thank you for your help

[snow crystal]

np

what grade are u in?

[upper karma]

i am going to 10

im trying to learn geometry so it can be easy for me next year

[snow crystal]

you never did geometry before?

[upper karma]

nope

this is all new for me

this is why i always come here to ask for help lol

[snow crystal]

ohh then my curriculum is waaayyy different

I would do some geometry every grade starting at 6

that's why I was shocked that you didn't know any of that stuff lol

[upper karma]

ohhh

[upper karma]

yea lmao

we start geometry at grade 10

so it's very weird

everyone else knows all of this so im suprised too

[snow crystal]

lol I'm going to 11 and we're about to start doing trig equations

polish curriculum be like

[upper karma]

ohhh

i might skip geometry and go striaght into algebra 2

[upper karma]

lol im in american curriculam

[snow crystal]

tf is algebra 2

we don't have that

[drowsy vector]

Algebra is focused on the concepts of algebra and solving equations etc, the basics of Algebra, while Algebra || is a bit harder, it touches things like logarithms, polynomials, quadratics, cubics, factorization etc

[lost marlin]

here in brazil everything is just algebra hahaha

[drowsy vector]

How’s your curriculum? Here it’s
9 Algebra ||
10 Geometry
11 Trigonometry
12 pre calculus(my school doesn’t offer it unfortunately)

[drowsy vector]

Doesn’t it get annoying? I’m tired of seeing letters all the time, fortunately I haven’t seen much Greek letters, just capital sigma, theta, alpha and beta

[lost marlin]

tbh it doesn’t. the only division we make is algebra (doesn’t matter if it’s alg I or II) and everything else

the curriculum here is kinda weird compared to the rest of the world

[drowsy vector]

The only division? Sorry I don’t follow

[lost marlin]

yes, we use mathematics I and mathematics II only

mathematics I is algebra and mathematics II is geometry/trigonometry

[drowsy vector]

I see

[lost marlin]

it’s actually pretty good

[drowsy vector]

Does calculus fall in math || or is that college level?

[lost marlin]

only in college, unfortunately

we get introduced to calculus on 12th grade, and it falls in math I

[drowsy vector]

Where I study calculus was given, then it went down to pre calculus and now it’s just a general math in 12 grade if you aren’t in an AP class

[drowsy vector]

[lost marlin]

most of pre calculus stuff we learn from 8th to 9th grade

trigonometry, polynomials, functions, etc

10th, 11th, and 12th grade here are just to get deeper in everything we had learn in the years before

[drowsy vector]

We have an AP class that introduces us to pre calc in 12 grade that shows us limits, functions, inverse functions, curves, area and just the basics of calculus

I’m currently going into AP trigonometry in 11 grade that gets me ready for next AP class for the introduction to pre calc but it’s still disappointing to see I can’t learn calculus in high school

[lost marlin]

yes, it’s a bit sad

i recently bought some books to learn calculus and linear algebra

hope it goes right

[drowsy vector]

Ohhh what books? I’ve learned calculus already but I’m looking for something else to learn like idk, advanced calculus or something else

[lost marlin]

calculus, by james stewart and linear algebra with applications by howard anton

[drowsy vector]

Mhmmm good stuff, I’ve learned calculus from Calculus for dummies and the essence of calculus

[lost marlin]

was it good?

[drowsy vector]

Which one?

[lost marlin]

any of them

[drowsy vector]

Calculus for dummies good, I liked how they gave really good explanations with physics which is nice, while the essence of calculus is a really good series on YouTube about differential calculus and integral calculus

[lost marlin]

good

where r u from?

[drowsy vector]

Freedom land

[lost marlin]

usa?

[drowsy vector]

Yup

[lost marlin]

cool

[deft drum]

So using this figure I derived $$\tan(A \pm B) = \frac{{\tan(A) \pm \tan(B)}}{{1 \mp \tan(A)\tan(B)}}$$

[somber coyote]

.tbhaxor

[deft drum]

So in the book from which I am reading this, they say that the angle $θ_{12}$ between two such straight-line graphs is equal to the difference in the angles they individually make with the x-axis. Lets say line 1 makes $\theta_1$ and line 2 makes $\theta_2$ then angle between two lines is $\theta_1 - \theta_2$. So if here line $A = \theta_1$ and $B = \theta_1 - \theta_2$ then $A - B = \theta_2$ or $ A + B = 2\theta_1 - \theta_2$.

[somber coyote]

.tbhaxor

[deft drum]

Then does we have this eq

Please help me understand it

[tall coral]

After doing some angle work, this one specifically caught my eye because I don't think it's actually possible for the two marked angles to be the same integer input with the rest of the given information

am I losing my mind or is there just a typo in my textbook??

[upper karma]

oh what

[upper karma]

mine is 9=algebra 1. 10=geometry or algebra 2(only if you skip geometry). 11=Alegbra 2 or pre-calculas or Ap calculas. and 12-Business math,stats, or Ap calculas AB and BC

did i do this right?

[zealous bolt]

When a side BC of a triangle ABC is produced to an exterior point D, answer

1. Write down the relation between <angle>ABCD and <angle>ABC+<angle>BAC
2. Verify experimentally that the relationship between <angle>ACD and <angle>ABC + <angle> BAC
3. If the triangle ABC is an isoscaled right angled triangle right angled at B, find the ratio of measurements of <angle> ABC and <angle>ACD

[upper karma]

whats this

[zealous bolt]

geometry triangle?

[upper karma]

im just asking if my answer is correct for this problem

[zealous bolt]

HELP

[snow crystal]

Yes

[upper karma]

okay thanks

[upper karma]

Is the answer 119?

[mystic charm]

Yes that's correct

[upper karma]

okay thanks

[upper karma]

how do i do this?

[willow night]

Diagonals of a parallelogram bisect each other

[upper karma]

yea ik that

how do i find the answer

[willow night]

What do we mean by bisect?

[upper karma]

do i just do 7x+2=6x+9

[willow night]

What do you think

[upper karma]

splitting something into 2 parts

[willow night]

2 equal parts yes

So yeah 7x+2=6x+9

[upper karma]

ohhh

so the answer is d

what is the answer to this

[lone panther]

obviuosly

[upper karma]

d was wrong

[lone panther]

it asked which statemnt is false;

[wind coral]

dont give out solutions

[upper karma]

yea D is wrong

I just checked it and i got 0/2 points for putting D

[lone panther]

b?

[upper karma]

prob i cant re check after submisson

[lone panther]

it doesnt show the correct answer?

[fervent vessel]

posting this again here from maths discussion since they are busy over there, i wanna know how many triangles you see here, my final count is 26

for context, my girlfriend was playing roblox and she sent me this, i dont play roblox so i have no idea what she was doing exactly but she told me that the game said the answer was 118 and i was like there's no chance. but I've been struggling to find a definitive answer

oh shit nvm I've seen 2 more and now i have 28. but surely can't be any more?

[snow crystal]

118? aint no way

also when you get past 20 it's pretty hard not to forget which triangles you've already seen and which you haven't lol

[snow crystal]

#book-recommendations

[upper cloud]

ohh sry

[summer spire]

most reliable way would be to label every vertex, iterate through every combination of 3 of them, and count if it makes a valid triangle

usually these problems are posed with rectangles, and there's a trick that makes those easy, but idk of any shortcuts with triangles like these

[willow night]

The problem is it's not quick and easy to remove all those combinations where we chose 3 collinear points

That are collinear

Like it's 11C3 - something, and calculating this something is a headache

And of course counting them one by one manually is dubious

[whole venture]

D is true and the question is looking for the anwser choice which is false

[upper karma]

nope

[upper karma]

yea

[fervent vessel]

this is how i worked it out in the end, i labelled each corner, every point the line segments intersect, and also each end of the lines that make a plus shape. so essentially like labelling 4 separate rectangles and then pushing them all together with their vertices labelled. though I looked at it by picturing 2 squares joined together.

A F B

E I J K G

D H C

if you can picture that lol thats how i labelled it, then just went through every unique combination of points like you said. first i did all the points involving the outer vertices on the left side, AFHDEIJ (confusing labelling ik). so i easily worked out there's a right-triangle in every corner, and 2 equilateral triangles that have the horizontal line going through. that made 6, along with all the inner triangles, (which i described as 'sub triangles') which is another 6, so each square has 12 total triangles. after joining them together you then have a diamond shape FKHI which makes an additional 4 triangles: AHB, DFC, IFK, and KHI. Sorry ik my labelling is the worst but i'm special okay

apologies for the long message

[summer spire]

so your final answer is... 52?

[upper karma]

Why is geometry so hard to understand

algebra is ez to do

but geometry is so painful

[fervent vessel]

no? 28

split the shape in half you hace 12 triangles in each square(or rectangle) so join them up you have 24 plus an extra 4 that are created once they are joined

[lucid moth]

I'm having troubles with this proof

[dawn swallow]

I haven't done Geometry in a while, I'll still try to do what I remember.

[lucid moth]

Sure ^^

[dawn swallow]

The triangle is isosceles.

An isosceles triangle has two congruent sides, in this case it is AB and AC.

The two base angles of an isosceles triangle are congruent, so <C and <B are congruent.

Next we will try to prove that Triangele EBC and Triangle DCB are congruent. We already know that <B and <C are congruent to each other from before.

EC and DB are also congruent to each other, because if AB and AC are congruent, EC and DB are congruent.

Finally, BC is congruent to BC because of reflexive property. The whole triangles EBC and DCB are congruent because of SAS (Side Angle Side).

---

Next, we will try to prove that triangle AEG and ADG are congruent to find <1 and <2.

We already know that Triangles EBC and DCB are congruent, so their sides GE and GD are congruent by CPCTC (Corresponding Parts of Congruent Angles are Congruent).

Next, AG is congruent to AG because of reflexive property.

We already know AE and AD are congruent.

So now we know that triangle AEG and triangle ADG are congruent to each other.

Finally, we can say <1 and <2 are congruent because of CPCTC.

Sorry if this took a long time, I was trying to make it make sense.

I am aware this probably isn't the fastest method to do it either.

I should probably go and brush up on my Geometry skills, I haven't done it in some time.

[lucid moth]

its okay I tried to do it on my own and Idk how but ended trying to explain why its a kite 💀

Thanks

[dawn swallow]

Wait what?

😂

[lucid moth]

yeah umm lets not talk about that

[dawn swallow]

Alright...

[lucid moth]

😭

[lucid moth]

So could I use the subtraction postulate to explain why EC and DB are congruent? AB - AD= AC- AE => DB = EC

[lucid moth]

nvm thanks for the explanation i found it really easy to follow 👍

[river abyss]

Is honors geometry hard? I am taking it for my freshman year this year. What should I know?

[lucid moth]

Personally I think its pretty easy, I'm taking it over the summer and taking regents at August. https://www.nysmathregentsprep.com/uploads/6/2/3/2/62326735/final_3_-_geometry_[common_core]_regents_review_sheet_-_facts_you_must_know_cold.pdf

The link above summarizes/contains most of the topics I thin

[river abyss]

Thank you this is really helpful

[strange vine]

I found the solution to this question, but i still dont get it. Can someone explain. Here is the question --> A right-angled triangle with integer side lengths has one side with length 605. This side is neither the shortest side nor the longest side of the triangle. What is the
maximum possible length of the shortest side of this triangle?

Here is the solution :

[stark ether]

can someone check my work?

[smoky jetty]

idek if this is correct but i did this: (11!)/((8!)(3!)); and got 165

[light skiff]

just spread them out 11 10 9 8 7 6 5 4 3 2 / 8 7 6 5 4 3 2 3 2 and start canceling stuff out

so 11 10 9 /3 2

so ye 165

[smoky jetty]

yeah i do that sometimes when in a hurry

[light skiff]

u dont rly have to write them down its faster in ur head lol

[smoky jetty]

lol my mental arithmetic aint the best

[light skiff]

ok think of it as diffrence between 11 and 8 is 3 so pick last 3 and multiply them

the 3! is just another part to do

[deft drum]

Could some one help me understand this question?

From this, it looks like pattern of $\sin(A + B)$, since first one is $\theta$, it has to be $\sin{\theta + B}$

[somber coyote]

.tbhaxor

[deft drum]

So far I have reached to have some arbitratry values like $a = K \cos{\phi}$ and $b = K \sin{\phi}$

[somber coyote]

.tbhaxor

[deft drum]

Which gives two relations $K^2 = a^2 + b^2$ and $\tan{\phi} = \frac{b}{a}$

[somber coyote]

.tbhaxor

[deft drum]

Also if we divide $a/b$ we get $\tan{\phi} = \frac{b}{a}$ which gives $ b = a\tan{\phi} $ and $K = \pm a \sec{\phi}$

[somber coyote]

.tbhaxor

[deft drum]

Now when I will put this in the equation where $k = K \cos{\phi}\sin{\theta} + K \sin{\phi}\cos{\theta}$, gives me $k = a (\sin{\theta} + \frac{b}{a} \cos{\theta})$.

[somber coyote]

.tbhaxor

[deft drum]

From here I am stuck now

[lean socket]

if a is cos and b is sin how is K anything other than 1

[deft drum]

Why do you think it should be 1?

I am just generalizing the term

[lean socket]

I know, but $\sin^2(x)+\cos^2(x)=1$ no matter x

[somber coyote]

hushus

[deft drum]

Yes it is you are 100% correct

[lean socket]

you are thinking of $r^2 \sin^2(x) + r^2 \cos^2(x) = r^2$

[somber coyote]

hushus

[deft drum]

$a^2 + b^2 = K^2 (\sin^2{\phi} + \cos^2{\phi}$ does this make sense?

[somber coyote]

.tbhaxor

[deft drum]

Exactly now what is $r \sin{x}$? its a

[somber coyote]

.tbhaxor

[deft drum]

so we safely replace it with $a^2 + b^2 = K^2$, isnt it?

[somber coyote]

.tbhaxor

[lean socket]

no because you chose a and b to be pure trig functions without scaling, so it will be 1

[deft drum]

Oh my bad its typo bro

[lean socket]

you said $a = \cos \phi$ and $b = \sin \phi$, regardless of $\phi$ it will be $a^2+b^2=1$

[somber coyote]

hushus

[lean socket]

ah i see

u fixed it

[deft drum]

Thanks for pointing out, in notebook I wrote scaling factor

[lean socket]

woops that second k at the end should be a different letter

it's not the same k as in this start, just an integer for the periodicity

[deft drum]

its $k \in N$. in second last right?

[somber coyote]

.tbhaxor

[lean socket]

yea i wrote it on the bottom right $k \in \mathbb{N}$

[somber coyote]

hushus

[deft drum]

Felling sleepy will check tomm

[lean socket]

no problem! but just make sure you use a different letter, it's not the same k

[deft drum]

sure

[sweet quiver]

is trig more geometry or alg

[snow crystal]

I'd say beginner trigonometry is more about geometry

But with time there is more algebra in it

[upper karma]

Would someone mind helping me figure out what a sinusoid is?

[dull light]

sine curve but it can be shifted in both axes or multiplied etc

for example 2sin(2x-3)+2 is a sine curve

note that cosine curves are also sine curves

Basically a sine curve but you play around with it

Although it retains its general shape

[upper karma]

Thank you

[zealous bluff]

wtf does x equal

[pastel thorn]

anyone know how to find the hyperbolic tangent of a matrix

[frozen ocean]

[tanh=\frac{sinh(x)}{cosh(x)}=\frac{e^{2x}-1}{e^{2x}+1}]

[somber coyote]

Akira

[proper nacelle]

Compute element-wise and replace with value

[pastel thorn]

how to you evaluate e^matrix though

[proper nacelle]

Thats ambiguous

Exponentiatation techniques I guess 😭

[pastel thorn]

trying to find tanh([5.5])
[-1]

[proper nacelle]

Apply the hyperbolic tangent function to each element and then replace each element in the original matrix with its corresponding hyperbolic tangent value

5.5 and -1 individually

[pastel thorn]

okay that makes sense

[cosmic violet]

Hey everyone. I’ve been reading book 1 of The Elements and I was wondering something. For example in proposition 1 when Euclid constructs an equilateral triangle from a given line, what exactly was proven here? Is this an existence proof? I.e., could we not assume the existence of equilateral triangles prior to proving this proposition? Or is its use purely as a tool for proving the other propositions, like I.5, which logically depends upon it? http://aleph0.clarku.edu/~djoyce/elements/bookI/propI1.html

[heavy crow]

Taylor series

$e^x\defeq\sum_{n=0}^\infty \frac{x^n}{n!}$

[somber coyote]

nixxy nilpotent (raving lunatic)

[heavy crow]

this is a vector, so your question is not correctly posed. generally when we talk about evaluating a function with a matrix, we are assuming a square matrix.

you just compute it element wise if it's a vector I guess.

[midnight bay]

What is 5 + 5 I’m new to math

[heavy crow]

#prealg-and-algebra but I'm guessing you're just trolling

[midnight bay]

Is it 12

[heavy crow]

ha ha hee hee hoo hoo

[midnight bay]

Wait no 15

[heavy crow]

this channel is for actual questions

[midnight bay]

Ok fine

[deft drum]

In my solution book the second line is written as $\sin^{-1}{\frac{k}{K}}$. It doesnt make sense to me please help

[somber coyote]

.tbhaxor

[deft drum]

Its machine learning @heavy crow 😅

[upper karma]

a) 283, b) 055, c) 15.4, d) 20.08

got confusion in part E

[lost jungle]

So I’ve been using khan academy to learn geometry and I was wondering if there were any other better ways to learn

[plush karma]

Youtube

[lean socket]

What is capital K? In the question there is only a, b, theta and k

[deft drum]

Its some assumption

[lean socket]

Give me some time and i’ll come back to it, i’m out of the house for a while. Is that ok?

[deft drum]

Sure

[lean socket]

what is the second line in my picture, when b is 0?

@deft drum maybe this is what you are expecting

[deft drum]

Yes exactly this thing

[indigo escarp]

Can I pls get the working out just to check if mine is right

[lean socket]

show yours, because there are multiple ways to do this type of question

[lean socket]

okay

[deft drum]

Thank you

😄

[lean socket]

np, my answer from yesterday is the same by the way, just some algebra and trig needed to get from that to this

if you plug in actual numbers you will see they are the same

[deft drum]

Yeah it comes with practice. I will do more practice on trig questions

[lean socket]

when it comes to trig, find the approach most comfortable and intuitive to you. there are always multiple ways to do them and it's about what you can recognize first

for example, you could check the answers here:
https://math.stackexchange.com/questions/3844215/how-to-solve-a-sin-theta-b-cos-theta-c
https://math.stackexchange.com/questions/2502976/solving-a-sin-theta-b-cos-theta-c

[deft drum]

To be honest I liked your first approach its easy, but didnt match answer key so I thought either you or I didnt understood question and approach 😅

[lean socket]

i like my first approach becausae i dont have to introduce arbitrary constants like K

just working with what is given

[deft drum]

Oh great now I feel more embarrassed the question was already asked lol

[lean socket]

hahaha no, don't feel embarrassed. You learned from this anyways!

majority of questions you will arrive to in trig have already been asked, i just googled "solve a sin theta + b cos theta =c" and then look for the stack exchange links

[indigo escarp]

I need to check my working

Can u send an answer pls

[indigo escarp]

It might be completely wrong

Cause I’ve nvr really done vectors

[lean socket]

check question 5's solution on this link. it's on page 4, same scenario but an airplane. I'm out so I can't check the work thoroughly

https://www.ketteringschools.org/userfiles/2182/Vector Word Problems.pdf

[indigo escarp]

Thnx

[lean socket]

Look at the solution of exercise 3 too

[upper karma]

hey iu have question

4x+3= 23

what is x can smbdy tell

does this come under geometry or trigonometry

[silent plank]

neither

it comes under algebra

[rustic yew]

are u 7?

guys help

how

my school didnt give me a formula

halp

[lost marlin]

there are 2 inscribed angles

the arch projected by the inscribed angle is double the angle itself

take the extremes points of those lines that forms these angles

this will be your arch

so x projects a 142 degree arch and y projects a 130 degree arch

how much is x and y?

[past matrix]

Any help to get on my problem? #help-1 message

[rustic yew]

bro howw

ik line AD is 5

but how u get line CB

<@&286206848099549185> pls help

[rustic sail]

So if I am remembering correctly, since all the lines are tangent lines, each common tangent should be equal

[lethal moss]

Why do you think so?

[rustic yew]

wait nvm

its not

[lethal moss]

Hello!

[rustic yew]

wsg

@lethal moss is it 6?

[rustic sail]

Yes

[lethal moss]

If what i have been told is correct, yes

[rustic yew]

so then the perimeter is 18?

[rustic sail]

AE=AD, CE=CF, and DB=BF

[lethal moss]

Why do you state so?

[rustic yew]

nvm

[willow night]

2(6+3+2) is the perimeter simply

[lethal moss]

I'm not telling you if your answer is correct, I am just asking why

[willow night]

Since the other segments are just equal to these

[rustic yew]

its 22

[lethal moss]

And problem solved

[rustic yew]

ayy

thx

my school is worse than discord at teaching lol

[lethal moss]

Do you have any other problems to solve?

[rustic yew]

no

thx tho

[lethal moss]

np

[past matrix]

Still not any closer to a solution to my problem 😂

[lethal moss]

What is your problem?

[past matrix]

#help-1 message

[wind coral]

<@&268886789983436800>

[light skiff]

What did he say @wind coral

[upper karma]

I don’t know nothing 💀💀

[whole venture]

You use the intersecting chords theorem

[upper karma]

Ok thanks

[wind coral]

It was just some guy offering money for someone to do his homework

[heavy crow]

i was referring to the person with the undergraduate role who was asking if 5+5 is 12 or 15

[prime berry]

PLS HELP RN

[cloud charm]

It's second option

50.92

[wind coral]

!nosols

[lime crown]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[light skiff]

law of sines

where uppercase is an angle and its corresponding lowercase is the opposite side

so for example if 62 is A 40 is a

@acoustic lark

[chrome relic]

what do they mean by this

its sideways im sorry

[carmine brook]

magnitude is used to measure the size of a number or a quantity. They used a weird word for this but its asking to find value of the two angles and length of side R

[glad cloak]

is everybody here in high school

[wind coral]

No

[glad cloak]

are there people in elementary school

[wind coral]

Definitely not lmao

It's against discord tos to be under 13

[glad cloak]

oh

im going to 7th grade and im doing alg 2/ trig

[wind coral]

Good luck 👍

[whole venture]

👶

[lethal moss]

Technically, yes, but in another education system (our "elementary school" has 8 grades)

[late monolith]

whats a locus

[warped bone]

Im doing evan chen book, Im trying to solve this one, any idea?

[snow crystal]

,rotate

[deft drum]

Yeah i know, in machine learning you never get right answer in first try

It's a meme 😅

[bleak blade]

@warped bone

AO=OC so angle CAO=ACO=(180-2*ABC)/2=90-ABC.
Thus, angle BAH=CAO

i was lazy to latex it

[smoky jetty]

is that an egmo book?

[smoky jetty]

oohh i could follow through some parts, but can u elaborate on "so angle CAO=ACO=(180-2*ABC)/2=90-ABC."?

i barely do proving problems in geo, oof

[bleak blade]

what do you need elaboration on

we have isosceles

And by inscribed angle theorem, angle AOC is 2*angle ABC

[upper karma]

Prove the inscribed angle theorem.

[warped bone]

nope, it's fine, I get it, Im trying to work with other problems now

[warped bone]

it's basically an isosceles triangle because each of those two segments are radius and ofc they have the same length

[warped bone]

ye I also know this one

[bleak blade]

Yep

[rustic yew]

What is the measure of each intercepted arc for each inscribed angle of a regular hexagon inscribed in a circle?

does anyone know what this means

<@&286206848099549185>

[dark sparrow]

@rustic yew is it the sentence as a whole that confuses you, or is it particular words that you don't know/understand

[rustic yew]

the sentence as a whole

@dark sparrow

is it 60 degress tbh I rly dont understand what its asking

[dark sparrow]

inscribe a regular hexagon in a circle.
look at each interior angle of the hexagon, and the arc it subtends in the circle.
what is the measure of each such arc?

[rustic yew]

I did

[dark sparrow]

can you show your diagram

[rustic yew]

alr

here

@dark sparrow

[dark sparrow]

ok great you did it as a compass and straightedge construction.

now mark one of the hexagon's angles and trace over the arc it subtends.

[rustic yew]

alr

@dark sparrow I did it

[dark sparrow]

show

[rustic yew]

ok

[dark sparrow]

this... is the same picture

[rustic yew]

I made the arc longer

u wanted me to do that right?

can u just tell me if it is 60 degrees?

[dark sparrow]

no, that is not what i wanted you to do.

no, the answer isn't 60°.

[rustic yew]

oh

ok

so like what should I do then

[rustic yew]

ohhh

so its 120 degrees then?

or am I just dumb

[dark sparrow]

no, it is not 120°.

[rustic yew]

ok

I dumb

[dark sparrow]

does this red arc, which i painstakingly traced over with my mouse, and which covers visibly more than half of the circle, look like 120° to you?

[rustic yew]

no

[rustic yew]

so whut do I do now?

[dark sparrow]

look at this red arc

tell me its measure

if you cannot tell me its measure, tell me what fraction of the circle it covers

[rustic yew]

2/3 of the circle

240 degrees?

@dark sparrow

[dark sparrow]

yes, 240 degrees, of course

[rustic yew]

thx so much @dark sparrow

this is so funny

why is discord teaching me more than my school

[dark sparrow]

underpaid teachers and greedy bosses

[rustic yew]

lol

[lost marlin]

lack of time in school, underpaid teachers, distractions in school, etc

[hollow bison]

how to take notes in maths digitally

[lost marlin]

use an apple pencil with an ipad

download goodnotes or notability

and take your notes

[upper karma]

arre paapu

aap?

learning math? lol

[late monolith]

Three straight lines will meet at the same point if the determinant of their terms is 0?

But how do I know what coordinate they intersect at?

[solid ledge]

yo when looking at similar triangles, do you experienced people use the vertex order of the similar triangles in order to determine the corresponding sides or do u just eyeball it

obviously assuming the vertices are written in the correct order

[silent plank]

don't eyeball

you should identify the corresponding components

[willow night]

Treat any of the 2 lines like a system of linear equations in 2 variables

And find the x,y where they intersect

[late monolith]

what about the 3rd line

[willow night]

If they're telling you the 3 are concurrent

The 3rd will undoubtedly pass through the same point

2 non coincident straight lines can at max meet at one point

You can pick any 2 of the 3 to solve for the point

It'll be the same

[timid rampart]

do I use cosine law or sine law

[dark sparrow]

what do you want to find?

@timid rampart

[timid rampart]

I wanna find the perimeter of ABC and then A

[dark sparrow]

ok, so you want to find the perimeter of ABC.

[timid rampart]

yup

[dark sparrow]

which element of the triangle are you missing from it?

[timid rampart]

I’m missing A C and b

[dark sparrow]

which element are you missing from the perimeter specfically?

[timid rampart]

A and C?

[dark sparrow]

what does the word "perimeter" mean?

[timid rampart]

The total length?

[dark sparrow]

it is the sum of the lengths of all your sides, yes.

which of A, C and b refer to a side?

[timid rampart]

b

[dark sparrow]

right.

so you want to find side b.

and you know sides a and c, and angle A.

so the elements you care about are three sides and one angle.

which law relates those elements? sine or cosine?

[timid rampart]

cosine?

[dark sparrow]

if you cannot answer right away, write out both laws and use that to guide your own choice.

yes, of course.

[timid rampart]

Thank you so much

❤️❤️❤️❤️

[lyric sonnet]

who has nice geometry questions

[storm portal]

Google does for sure

[lyric sonnet]

too lazy

[storm portal]

Oh no!

[wind coral]

Just search up "geometry worksheet" and you should be able to find some

[lyric sonnet]

still too lazy

[wind coral]

Oh well good luck finding one then, I ain't doing it for u

[lyric sonnet]

do you know presh talwalkar

[wind coral]

Yeah

[lyric sonnet]

https://www.youtube.com/watch?v=uJqbHaFqjmI

[lyric sonnet]

5 minutes

[wind coral]

?

I'm a bit confused

[lyric sonnet]

does the question look that hard

[wind coral]

That is a pretty subjective question but to me yes

[lyric sonnet]

bcos presh talwalkar couldn't solve it.

[bleak blade]

Which

[fossil spade]

what do i need to know to start learning trigonometry

[silent plank]

soh cah toa

[fossil spade]

anything else ?

[silent plank]

that's how you get started

basic algebra/geo would be assumed knowledge

[fossil spade]

alright thanks

i’ve got all of those

[lost marlin]

some pretty basics triangles properties

sum of intern angles, pytagorean theorem, etc

[upper karma]

can someone help me with law of cosines

like ik the formula is for angle a= a^2=b^2+c^2-2bc cos A

what is cos

and how do i solve it in a normal cqalculator

[snow crystal]

wdym "what is cos"

oooh I remember, you just started trig

cosine is one of six trig functions

just lmk what exactly you don't know

cause I'm unsure

[upper karma]

yea

um can u help me

so this is the problem

for a i did= a^2=4.78^2+9.24^2-2(4.78)(9.24)(cos 30.95)

[snow crystal]

what are you supposed to do here?

[upper karma]

solve fir angles a,b, and c

so ik how to use the formula

but the thing is

idk about the cos thing

what am i supposed to do with it

[snow crystal]

ok so you have to find the area right?

[snow crystal]

I'm not english and idk what "solve for" means

[upper karma]

no

[upper karma]

find the angles

i think

[snow crystal]

but all angles are given

@upper karma

[upper karma]

we have to calculate the Law of Cosines for angles A, B and C

[snow crystal]

fair enough

[snow crystal]

you made a mistake

it should be cos 65.17

[upper karma]

wait why

the formula says Cos A

cos a is 30.95

[snow crystal]

alpha is not the same as A

A is a vertex of the triangle

and Beta is the angle created by sides b and c

[upper karma]

wait so

Cos b is 30.95

and cos c is 83.87

[snow crystal]

yeah

[upper karma]

ahhh

then how do i solve the cos

[snow crystal]

you can always use this $\sin^{2}x+\cos^{2}x=1$

[somber coyote]

iammax420

[snow crystal]

because you know sines of those angles

[upper karma]

the teacher told us we can only use the one i used above

[snow crystal]

ok so what you did for A was correct but you have to use cos 65.17 instead of 30.95

and do the same thing with 2 other angles

[upper karma]

wait look

@snow crystal this is what i did

but idk how to solve them in the calculator with the cos feature

so what do i do

[snow crystal]

you forgot to substitute a with 8.43

[upper karma]

where

[snow crystal]

wdym where

in the work you just sent

[upper karma]

what problem

1 or 2

[snow crystal]

one...

if your task is to find the cosines of these angles you have to plug in all sides lenghts

[upper karma]

yeah

[snow crystal]

there is no point of finding values of sides a, b and c if they're already given

[upper karma]

in number 1 im finding angle a

[snow crystal]

can you do vc rn?

[upper karma]

no srry

[upper karma]

i did the work but idk how to solve cos in the equation thats all i need help in

[snow crystal]

this is for A

now you just multiply stuff, substract, divide and that's it

got it?

[upper karma]

divide what

why is 8.43 there

[snow crystal]

wait, I made a mistake here

[upper karma]

the teacher didnt do that in her example problem

[snow crystal]

this is the actual law of cosines if you want to evaluate cosine A

all side lenghts are given

idk what your teacher did but this is correct

[upper karma]

yea

im doing that

so um

i got 108.226-88.3344xcos 65.17

how do i solve it after

[snow crystal]

substract 108.226 from both sides

I'm not sure if you understand how law of cosines works

if you have time we can vc and I'll explain it to u

cause I don't want to write an essay here

[upper karma]

i dont

[upper karma]

hmm okay

so 88.3344xcos 65.17-108.226

[snow crystal]

no

it's just 88.3344xcos 65.17

[upper karma]

ohh

[serene mulch]

confusing

[wind coral]

what exactly are you confused about?

[serene mulch]

dm

[wind coral]

we can do this here

[serene mulch]

okay

Brian served 3 spherical scoops of ice cream each with a diameter of 3 inches

how much money would he charge if each cubic inch costs 8 cents ?

I don’t know how to find the cost if each cubic inch costed 8 cents

[wind coral]

have you done anything with the question so far?

[serene mulch]

no

dont know where to start

[wind coral]

we can start by finding the cubic inches of one of the scoops

[serene mulch]

ok each scopp has a diameter of 3 inches

[wind coral]

yep

do you know the formula that is supposed to be used in this question?

[serene mulch]

V=4/3x(3.14)r3

[wind coral]

use * for multiplication and ^ for exponets btw

but other than that yes

use that formula to find the volume of one of the scoops

[serene mulch]

ok ok

isnt half of the diamter the radius ?

[wind coral]

yep

[serene mulch]

37.68 in3

?

[wind coral]

what u said before, the radius is half the radius

[serene mulch]

oh

i tweeked

[wind coral]

so we wouldnt use 3 for the radius

[serene mulch]

hold up

1.5

[wind coral]

yep

[wind coral]

correct

[serene mulch]

thank you man

[wind coral]

np

but were not quite done yet

[serene mulch]

ok ok

[wind coral]

we have the volume of 1 one the cones

but we have three cones so what do you think we should do to find the volume of all 3 of them?

[serene mulch]

same thing ? woudlnt it be the same answer

[wind coral]

all three of them combined, mb

[serene mulch]

oh wouldnt i just add ? the 14.109

3x

[wind coral]

yep, or multiply 14.109 by 3

[serene mulch]

42.327

[wind coral]

yep

wait a sec though i found a mistake that i didnt catch before

[serene mulch]

yeah 8 cubic inch cost cents

i think

[wind coral]

here when you did 1.5^3 you might have done it wrong

1.5^3 doesnt equal 3.317

[serene mulch]

3.375

[wind coral]

yep

so do the operations you did before but with 3.375

[serene mulch]

ohh 14.13

it says if each cuubic inch costs 8 cents

[wind coral]

we shouldnt be to that part just yet

we should find the volume of the cones combined

then do that

[serene mulch]

42.39

[wind coral]

yep

now see how much it costs

[serene mulch]

divide by 8 ?

or x

[wind coral]

nope, there is 8 cents for each cubic inch

[serene mulch]

42.39 is the cubic inches ?

[wind coral]

ye

[serene mulch]

1 scoop = 14.13

3 scoops = 42.39

oh hed charge 42.39

[wind coral]

42.39 is the volume of 3 scoops, not the cost

[serene mulch]

okay we got the volume

what do we do with the 8 cents

[wind coral]

what do you think? if there is 8 cents on one cubic inch, 16 cents in 2 cubic inches... how many cents would be in 42.39 cubic inches?

[serene mulch]

336

cents

[wind coral]

close, you shouldnt have gotten a whole number

[serene mulch]

ohhhhhh

339.12

?

[wind coral]

yep

[serene mulch]

hed charge $339.12 if each cubic inch costed 8 cents

thanks man man

[wind coral]

wait

not quite, remember were working with cents, not dollars

[serene mulch]

the question is asking how much money would he charge if each cubic inch costed 8 cents

[wind coral]

yeah you have 339.12 cents

not 339.12 dollars

[serene mulch]

ohh

thanks

[wind coral]

np :)

[wind coral]

you should give it a shot before coming to us for help. the best way to learn this sort of material is with logical problem solving on your part

[still jay]

any advice on how to solve trigonometry limit questions? currently struggling with one right now because of indeterminate

couldn't find any identities that could make the term somehow not indeterminate, I suck at trigonometry basically

[snow crystal]

can you post the problem here?

[still jay]

oh there's a latex bot in this server

$$ \lim_{x \to 0} \dfrac{2\sin(5x)}{\tan(2x)}$$

[somber coyote]

Lyerix

[snow crystal]

damn that looks tough

[still jay]

tho I'm asking in general, on how to solve the indeterminate

[still jay]

it looks easy at first, but then it's difficult as hell

[indigo escarp]

For q9

How do I draw the diagram?

[snow crystal]

have you tried l'hospital?

[still jay]

this is my first time learning this material and my teacher already gave us this question 🤦 he didn't even teach us anything about this besides just a YouTube video (just one), and the video only solves for easy problems

[still jay]

therefore I can't use L'Hopital

I would, I know how, but my teacher probably won't let me, hence futile

[snow crystal]

I'll try to solve it

[still jay]

thanks man, I appreciate it

I'm at my 6th attempt now

[snow crystal]

so far I have this and I might try a different approach

I'll be away for like 1,5h but I asked my teacher how she would solve it so hopefully she responds today

ok so she advised me to either transform it to the point I get something better or use l'hospital

[still jay]

thank you, man. I'll look forward to it

[obtuse jay]

How do i turn 0.75 radians into degrees mins seconds?

[indigo escarp]

@marsh copper

[marsh copper]

ya

[indigo escarp]

I can’t access help 9

I still don’t get by Wym

Wind coming at north t east

I thought it’s coming from 70

[marsh copper]

it is coming towards north east

[marsh copper]

ya but you need diagram right

[indigo escarp]

Is this Wym

[marsh copper]

|

like wait one sec

[marsh copper]

like thats approx direction in which wind is blowing

north west one

@indigo escarp

[indigo escarp]

Huh

Is that diagram right

I hv no clue

[marsh copper]

lol

||aaaaaaaaaaaaa|| |
||aaaaaaaaaaaaa|| |
||aaaaaaaaaaa|| /||.|| \

||aaaa|| wind /////

[little kiln]

huh?

[marsh copper]

like it is a diagram

[indigo escarp]

Bro what ru typing

[marsh copper]

dont see spoilers

you think it like a diagram

[indigo escarp]

Oh

How to unsee spoilers

[marsh copper]

wait some time

or go to some other server and come back here

[indigo escarp]

Bro

That does not make sense

[marsh copper]

|
|
|\ this is an air craft

///// this is wind

now did you understand

[little kiln]

no

[indigo escarp]

Pls

Can u explain

[upper karma]

for these questions

[upper karma]

for 1 is it 28+45+90+x=180

and 2 80+64+90+x=180

and 3 56+x+106+90=180

did i do them right

[wind coral]

i think you are mixing up angle properties with sides

Pythagoras theorem should be applied here

[upper karma]

oh

so what should i do

[wind coral]

are you familar with pythagoras theorem?

[upper karma]

yes

a^2+b^2=c^2

[wind coral]

yep

use that rule to solve for the missing side

[whole venture]

These are right triangles so you can directly use the pythagoras theorem here

[upper karma]

so 28^2+45^2=x?

[wind coral]

very close, 28^2+45^2=x^2

[upper karma]

ahhh

[upper karma]

and for q 2 it's 64^2+80^2=x^2

[wind coral]

not quite

[upper karma]

and 3 is 56^2+106^2=x^2

[upper karma]

wait why

[whole venture]

Shouldn't there be a positive and negative solution for x 👀

[wind coral]

were not trying to find the hypotenuse

rather one of the legs instead

[upper karma]

yea

i used the pythagreom thream

[wind coral]

yeah there would be according to desmos but it wouldnt make sense to have a negative side length

[upper karma]

ah so what should i do in 2?

[wind coral]

on number 2 we know the hypotenuse is 80

so c=80

[upper karma]

yes

[wind coral]

not b

[upper karma]

yea so

what wpuld the equation be?

[wind coral]

well look at the known values

one of the legs has a length of 64

[upper karma]

yea

[wind coral]

and the hypotenuse has a length of 80

so a^2+64^2=80^2. a being the missing leg length

[upper karma]

oh

so i find a

in this 2

right?

[wind coral]

yep

[upper karma]

ahh so

[wind coral]

for 3 it would be very much the same

[upper karma]

a=48

[upper karma]

so i find a in 3?

[upper karma]

isn't 3 more like 1?

[wind coral]

its more like 2

[upper karma]

oh

[wind coral]

the triangle is rotated in such a way to trick you

[upper karma]

so a^2+56^2=106^2?

[upper karma]

ohhhh

thanks

[wind coral]

np, what did you get for your 3 answers so i can be sure

[upper karma]

for 1 i got x=53

for 2 a=48

for 3 a=90

are they right?

[wind coral]

yep all good

[upper karma]

for this do i do a^2+14^2=25^2

[wind coral]

pythag only works with right triangles so no

but it has been kindy split into right triangles for us already

[upper karma]

yes

[wind coral]

we just need to find the length of the other leg

[upper karma]

so do i need an equation for that?

[wind coral]

not really, the line bisects the bottom side of the triangle and splits it evenly

use that fact to find the this leg length

[upper karma]

aren't we sippossed to use BxH/2

?

[wind coral]

not yet

[upper karma]

we dont have the height

nvm

[wind coral]

were trying to find the height using pythag

currently though, we need to find the base of the right triangle

[upper karma]

yea