multiple choice 1 point\nevaluate without using a calculator by using ratios in a reference…

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

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

Answer

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})