# Thread: Solving for x with a trig function

1. ## Solving for x with a trig function

How do I solve for x when f = 4(-cos^2(x) + sin^2(x) + sin(x))?

I can regroup the function in various ways, and I factored out the 4 already, but I don't know how get the function so that I can solve for x... If you get me started on the right path, or hint at an identity that I can use, that would help. Thanks.

2. Originally Posted by Maziana
How do I solve for x when f = 4(-cos^2(x) + sin^2(x) + sin(x))?

I can regroup the function in various ways, and I factored out the 4 already, but I don't know how get the function so that I can solve for x... If you get me started on the right path, or hint at an identity that I can use, that would help. Thanks.
$\displaystyle -cos^2(x) = -(1-sin^2(x)) = sin^2(x)-1$

$\displaystyle 4(sin^2(x)-1+sin^2(x)+sin(x)) = 4(2sin^2(x)+sin(x)-1)$

This is now a quadratic in sin(x)

3. f(x) = 4(-cos^2(x) + sin^2(x) + sin(x)) = 4(2sin^2(x)+sin(x)-1),

y = f(x) = 4(2sin^2(x)+sin(x)-1), or 4(2sin^2(x)+sin(x)-1) = 0 if you want to solve for the roots.

USE QUADRATIC FORMULA: solve for x then, . . . . see graph of the function