Answer
a) $30^{\circ} + 360^{\circ}k$ and $150^{\circ} +360^{\circ}k$, for all integers $k$.
b) $30^{\circ}, 150^{\circ}$
Work Step by Step
b) Isolate $sin\theta$
$2sin\theta = 1$
$sin\theta = \frac{1}{2}$
2. Recall angles from the unit circle $sin\theta$ is positive in quadrant I and II
$30˚$ and $150˚$ is when $sin\theta = \frac{1}{2}$
Therefore, $sinθ = \frac{1}{2}$ $\theta = 30˚, 150˚$
a) Take the two angles and add $360^{\circ}k$, where $k$ is an integer, to find all degree solutions.
$30^{\circ} + 360^{\circ}k$ and $150^{\circ} +360^{\circ}k$, for all integers $k$.
