Question

multiple choice 1 point
evaluate without using a calculator by using ratios in a reference triangle.
sin\frac{5\pi}{6}
-\frac{\sqrt{2}}{2}
\frac{\sqrt{3}}{2}
\frac{1}{2}
-\frac{\sqrt{3}}{2}

Explanation:

Step1: Determine the reference angle

The angle \(\frac{5\pi}{6}\) is in the second quadrant. The reference angle \(\theta_{r}\) is \(\pi-\frac{5\pi}{6}=\frac{\pi}{6}\).

Step2: Recall the sine value of the reference angle

We know that for the angle \(\theta = \frac{\pi}{6}\), \(\sin\frac{\pi}{6}=\frac{1}{2}\). In the second quadrant, the sine function is positive.

Answer:

\(\frac{1}{2}\)