2 multiple choice 1 point evaluate without using a calculator by using ratios in a reference triangle. sin…

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

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

Answer

Explanation:

Step1: Find the reference angle

The angle (\frac{5\pi}{3}) is in the fourth - quadrant. The reference angle (\theta_{r}=2\pi-\frac{5\pi}{3}=\frac{\pi}{3}).

Step2: Determine the sign of the sine function

In the fourth - quadrant, (\sin\theta<0).

Step3: Use the sine value of the reference angle

We know that (\sin\frac{\pi}{3}=\frac{\sqrt{3}}{2}). Since (\sin\frac{5\pi}{3}<0), then (\sin\frac{5\pi}{3}=-\sin\frac{\pi}{3}).

Answer:

(-\frac{\sqrt{3}}{2}) (the second option)