# Thread: Solving an equation in a specified interval

1. ## 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?

2. is the middle term $\displaystyle \cos(2\theta)$ or $\displaystyle \cos^2{\theta}$ ?

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

3. 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 $\displaystyle \cos^2{\theta}$.

Equation rewritten:

$\displaystyle \cos{\theta}$ + $\displaystyle \cos^2{\theta}$ + $\displaystyle \sin^2$.

4. $\displaystyle \cos^2{\theta} + \cos{\theta} + \sin(2) = 0$

only problem is $\displaystyle b^2 - 4ac < 0$