# How do you find the solution to 5(costheta+1)=5 if 0<=theta<360?

Jun 8, 2018

$\frac{\pi}{2}$ and $\frac{3 \pi}{2}$

#### Explanation:

I assume you know $0 \le \theta < 360$ is the same thing as $0 \le \theta < 2 \pi$

I will solve in Radians which are easier than degrees.

$5 \left(\cos \theta + 1\right) = 5$ on $0 \le \theta < 2 \pi$

$5 \left(\cos \theta + 1\right) = 5$

divide off the 5:

$\cos \theta + 1 = 1$

subtract the 1

$\cos \theta = 0$

now we look at the unit circle:

$\cos \theta = 0 \text{ at } \frac{\pi}{2} \mathmr{and} \frac{3 \pi}{2}$ on the interval $0 \le \theta < 2 \pi$