# Thread: Simplify for X? radian equation?

1. ## Arc Segments - Trig? Finding ratio (via golden angle)

Attachment 20346
This one has thrown me for a loop.
Basically I have to simplify and then solve for x where y is 1 and c is (1+√5)/2
and arc A = 2Pi(1 - 1/c)
2(arc A) + 2(arc B) equal a full circle.
I'm lost, any help is appreciated. Thank you.

2. 

Note that if $R$ was the radius, $Y = 2R\sin(B/2)$ and $X = 2R\sin(A/2)$.

So, $X=Y\frac{\sin(A/2)}{\sin(B/2)}$.

I think you should be able to go from there.

3. Using that I got A=2.3999632297287 and X = .38880073356013 if Y=1 ... I know this is not correct because x>y ... could you maybe expound upon that further simplifying A and B into the equation so I can see what's supposed to happen? thank you, I really appreciate your help

So basically I'm looking at it like this:
X=Y(cos(A/2)/cos(B/2)), Y=1, B=(2Pi-2A)/2, A=2Pi(1-1/c), c=(1+Root of 5)/2

Am I right about B at this first step?

4. Oops, it should have been sin and not cos.

5. Okay... so in that case I got x ~ 2.57... is that correct?

Edit:
Could someone help show me the step by step on how to solve this properly if you have the time and kindness? thank you.

6. I'm not that great adding drawings to posts, so I'll try to describe it.

To get $Y = 2R\sin(B/2)$, in the diagram, the rectangle is divided into 4 triangles. Look at one of these triangle with side length Y.
Bisect the angle of the triangle from the center of the circle, and you have two right triangles.

7. ## Trying to solve... ????

This is driving me nutty... okay so in that scenario the hypotenuse is the radius... however when I try to solve for X I get all wrong values... no matter which trig function I use... so what could I be doing incorrectly?