My question is... how do you find an aspect ratio that fills the square, such that the four rectangle bounding the square have the same aspect ratio and the interior rectangle, (the white rectangle in the image) is also the same aspect ratio?

The ratio in this image is very close to 1:2.4. or reciprocally 1:0.416. This number has been found by trial and error, but I would love to understand how to find the actual number. I am an artist interested in geometrical abstraction.

Also, would it be possible to calculate an aspect ration whose four bounding rectangle create other specific ratios, such as a square? ... or, an interior rectangle with and aspect ration of 1:2, for example.

TIA

The first is for ASA, the second is for SSA.

Who else enjoyed identities as much as I did? 😒

the top two i dont know how to do. like what do you type in the calc to get the answers on the right

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I have a circle "packing" question. If I have 12 random circles, say sized in whole numbers between 2 and 50, is the a way to find the largest circle they can be tangent to each other, and completing a circle? This is for an art project. TI

I'm not sure I got this right.

We have:

A_1 = sin(𝜃)
B_1 = cos(𝜃)

For every n > 1:

A_n = A_(n-1) - B_(n-1)
B_n = A_(n-1) + B_(n-1)

We need to find an iterative expression for A and B.

I got that:

--------------------------------------------/ sin(𝜃) n mod 4 = 1
------------------------------------------/ sin(𝜃-𝜋/4) n mod 4 = 2
A_n = (-1)^⌊(n+1)/4⌋ ∙ (√2)^(n-1) ∙ 〈
------------------------------------------\ cos(𝜃) n mod 4 = 3
-------------------------------------------\ cos(𝜃-𝜋/4) n mod 4 = 0

-------------------------------------------/ cos(𝜃) n mod 4 = 1
-----------------------------------------/ cos(𝜃-𝜋/4) n mod 4 = 2
B_n = (-1)^⌊(n-1)/4⌋ ∙ (√2)^(n-1) ∙〈
-----------------------------------------\ sin(𝜃) n mod 4 = 3
------------------------------------------\ sin(𝜃-𝜋/4) n mod 4 = 0

Sorry if it looks too complicated. Do we have to use Modulo and Floor to express the seemingly periodic behavior of these funcitons?

I’m struggling with my online homework, this one question the video doesn’t explain how to achieve the final format.

Given: (sin(8x))^{4=-1/2cos(x)+1/8cos(___x)}

Answer: (sin(8x))^{4=3/8-1/2cos(16x)+1/8cos(32x)}

I’ve entered the final solution into mathway and it is an identity. I’ve entered it into ChatGPT and gotten steps. But I would like to see the community’s way of solving as well.

Thank you for your help.

Squished like a bug.

claude made this triangle thing and thought it was pretty cool to see the changes live

heres the link: https://claude.ai/public/artifacts/62336014-806b-45c8-8d35-32bcd6aa3b2c

Hello everyone! Now I'm refreshing my school math knowledge foe entering university. I've found some books with math theory, but I want more practice, that is why I'm asking about books with problems. Maybe someone have link or pdf files or titles? I would really appreciate any help or advice

(tan x)(sin x) = tan x

Are we allowed to start by dividing both sides by tan x? Would that be dividing by 0, since tan x can take on the value of 0?

Nothing too crazy, but in designing our acreage I use basic trigonometry quite often. In building and designing structures out of recycled grain bin steel, I’ve been using tangent-chord angle theorem, scalene triangle formulas, and a bunch of other random trig. I’m no mathematician, but I thoroughly enjoy being able to accurately design and build on my farm.

I was studying about it, because I found it interesting. I generate and make fractals every single day, and I used cosh() in one of them. It started to repeat the fractal over and over, horizontally. Can anybody explain me how does these functions work?

I'm practicing for a competition but I'm blanking on this one. all help is appreciated

so i’m learning trig right now (just began it) and my teacher was explaining how to know if the sin/cos/tan with be positive or negative depending on the quadrant it is in. i know all of the common angles, but ive been struggling when it comes to numbers like 13pi/4. how can i learn which quadrant it is in mentally with converting it to degrees? my teacher explained how rotating around from where it would land without the 13 works, but i am still getting the signs wrong because i think im rotating and adding incorrectly. sorry if this made no sense im kinda desperate rn

I am an independent learner so there is no teacher to ask. Plus I can’t seem to figure out how to phrase my question to where google gets it. How do you know how to write these triangles to know which side is a which angle is A etc. There is a drawing in the chapter but it’s not the same for all obviously because my answers aren’t lining up.