# Solving an equation in a specified interval

• Sep 15th 2008, 05:45 PM
D. Martin
Solving an equation in a specified interval
The Question: Solve the equation in the interval 0 < θ < 2 pi.

cos θ + cos2 θ + sin2 = 0

Attempted Solution: Well, my hunch was to factor this equation. But, at least to my innumerate eye, it looks as if it cannot be factored. I am a bit confused by the structure of this equation. I'm not use to seeing anything like "sin" without a θ. The answers probably really easy and maybe it's just tiredness preventing me from seeing the solution, but could someone help?
• Sep 15th 2008, 06:26 PM
skeeter
is the middle term $\displaystyle \cos(2\theta)$ or $\displaystyle \cos^2{\theta}$ ?

btw, $\displaystyle \sin(2)$ is just a constant.
• Sep 15th 2008, 06:44 PM
D. Martin
Quote:

Originally Posted by skeeter
is the middle term $\displaystyle \cos(2\theta)$ or $\displaystyle \cos^2{\theta}$ ?

btw, $\displaystyle \sin(2)$ is just a constant.

It's $\displaystyle \cos^2{\theta}$.

$\displaystyle \cos{\theta}$ + $\displaystyle \cos^2{\theta}$ + $\displaystyle \sin^2$.
$\displaystyle \cos^2{\theta} + \cos{\theta} + \sin(2) = 0$
only problem is $\displaystyle b^2 - 4ac < 0$