How do you find the values of theta given costheta=sqrt2/2?

Feb 12, 2018

$t = \frac{\pi}{4} + 2 k \pi$
$t = \frac{7 \pi}{4} + 2 k \pi$

Explanation:

$\cos t = \frac{\sqrt{2}}{2}$
Trig table and unit circle give 2 solutions -->
$t = \pm \frac{\pi}{4}$
Note that $t = \frac{7 \pi}{4}$ is co-terminal to $t = \left(- \frac{\pi}{4}\right)$.
$t = \frac{\pi}{4} + 2 k \pi$, and
$t = \frac{7 \pi}{4} + 2 k \pi$