# Help to solve simple trigonometric equation

• September 14th 2010, 05:31 AM
AeroScizor
Help to solve simple trigonometric equation
Here's the equation: cos^2 ѳ-cos ѳ=2
I usually apply this set of method to solve such questions but it doesn't seem to work out this time round:
2)Find basic angle
4)Find values of ѳ
If you see what i mean.
• September 14th 2010, 05:33 AM
Prove It
$\cos^2{\theta} - \cos{\theta} = 2$

$\cos^2{\theta} - \cos{\theta} - 2 = 0$

$(\cos{\theta} + 1)(\cos{\theta} - 2) = 0$

$\cos{\theta} + 1 = 0$ or $\cos{\theta} - 2 = 0$

$\cos{\theta} = -1$ or $\cos{\theta} = 2$.

Since $-1 \leq \cos{\theta} \leq 1$ for all $\theta$, that means the second equation is impossible.

So $\cos{\theta} = -1$

$\theta = \pi + 2\pi n$ where $n \in \mathbf{Z}$.
• September 14th 2010, 05:40 AM
AeroScizor