# Solving for x with a trig function

• Oct 29th 2009, 01:58 PM
Maziana
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.
• Oct 29th 2009, 02:04 PM
e^(i*pi)
Quote:

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)
• Oct 29th 2009, 11:41 PM
pacman
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

(Bow)