# Trigonometric Equation

• Nov 11th 2012, 11:57 AM
derek1008
Trigonometric Equation
How do you solve the equation 5cos(2x)=2 ?
• Nov 11th 2012, 12:52 PM
MarkFL
Re: Trigonometric Equation
I would divide through by 5 first. Then I would solve the 2 cases (where $k\in\mathbb{Z}$):

a) $\cos(2x)=\cos(2x+2k\pi)=\frac{2}{5}$

b) $\cos(2x)=\cos(2k\pi-2x)=\frac{2}{5}$

Recall, if $\cos(f(x))=a$ then $f(x)=\cos^{-1}(a)$, where $a$ is an arbitrary constant.