# How do you find the values of theta given sintheta=1/2?

Mar 16, 2017

$\theta = \frac{\pi}{6} \text{ or } \theta = {30}^{o}$

#### Explanation:

$\text{if } \sin \theta = \frac{1}{2}$

$\text{then } a r c \sin \left(\frac{1}{2}\right) = \theta$

$\theta = \frac{\pi}{6} \text{ or } \theta = {30}^{o}$

Mar 17, 2017

$\frac{\pi}{6} + 2 k \pi$
$\frac{5 \pi}{6} + 2 k \pi$

#### Explanation:

$\sin t = \frac{1}{2}$
Trig table of special arcs gives:
$t = \frac{\pi}{6} + 2 k \pi$
Trig unit circle gives another t that has the same sin value -->
$t = \pi - \frac{\pi}{6} = \frac{5 \pi}{6} + 2 k \pi$