Trig Question

[Destiny of Pi]

I have a question:

if x = 2sin(x), then find the correct expression for cos.

Currently I have the answer like this: √(1-4sin^2(x)), how could I simplify it further?

[kw0573]

If x = 2 sin(x), then sin (x) = x/2. That means in a right triangle, opposite is x and hypotenuse (diagonal) is 2, That makes the third side ±sqrt (4 - x²) and so

cos (x) = ± sqrt (4 - x^2) / 2

Alternatively use sin²(x) + cos²(x) = 1, sin(x) = x/2, cos(x) = ± sqrt (1 - x² / 4) = ± sqrt (4 - x^2) / 2

Remember to never skip steps and plug in the proper expression. 

Edited April 10, 2017 by kw0573