what is the value of sine at 210°? √3 / 2 -√3 / 2 1/2 -1/2

Explanation:

Step1: Determine the quadrant

$210^{\circ}$ is in the third - quadrant ($180^{\circ}<210^{\circ}<270^{\circ}$), and sine is negative in the third - quadrant.

Step2: Find the reference angle

The reference angle $\theta_{r}=210^{\circ}-180^{\circ} = 30^{\circ}$.

Step3: Recall the sine value of the reference angle

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

Step4: Determine the sine value of $210^{\circ}$

Since sine is negative in the third - quadrant, $\sin(210^{\circ})=-\sin(30^{\circ})$. So $\sin(210^{\circ})=-\frac{1}{2}$.

Answer:

D. -1/2