Question

question given the following unit circle, rotate green dot to the appropriate angle and then find the exact value of the function. \\(\sin 150^{\circ}\\)

Explanation:

Step1: Determine the reference angle

The angle $150^\circ$ is in the second quadrant. The reference angle is calculated as $180^\circ - 150^\circ = 30^\circ$.

Step2: Recall the sine value of the reference angle

We know that $\sin 30^\circ=\frac{1}{2}$.

Step3: Determine the sign of the sine value

In the second quadrant, the sine function (which represents the y - coordinate on the unit circle) is positive. So, $\sin 150^\circ=\sin(180^\circ - 30^\circ)=\sin 30^\circ=\frac{1}{2}$.

Answer:

$\frac{1}{2}$