# Find all solutions if 0° ≤ θ < 360°. Verify your answer graphically. (Enter your answers as a comma-separated list.)? sin 2θ = −1/2

Aug 9, 2018

See below

#### Explanation:

Let’s say $2 \theta$ is equal to $u$:
$\sin u = - \frac{1}{2}$
$u = {210}^{\circ} \pm {360}^{\circ} n$
$u = {330}^{\circ} \pm {360}^{\circ} n$

Now let’s solve for theta:
$\theta = {105}^{\circ} \pm {180}^{\circ} n$
$\theta = {165}^{\circ} \pm {180}^{\circ} n$

Now find all feasible solutions by adding or subtracting ${180}^{\circ}$ to all the solutions:
$\theta = {105}^{\circ} , {165}^{\circ} , {285}^{\circ} , {345}^{\circ}$