Problem

Find the exact value of $\cos \frac{5 \pi}{6}$.

Answer

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Answer

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

Steps

Step 1 ：Find the reference angle for \(\frac{5 \pi}{6}\) by subtracting \(\frac{\pi}{2}\) from \(\frac{5 \pi}{6}\):

Step 2 ：\(\text{reference angle} = \frac{5\pi}{6} - \frac{\pi}{2} = \frac{\pi}{3}\)

Step 3 ：Find the cosine of the reference angle \(\frac{\pi}{3}\):

Step 4 ：\(\cos \frac{\pi}{3} = \frac{1}{2}\)

Step 5 ：Since \(\frac{5 \pi}{6}\) is in the second quadrant, the cosine will be negative:

Step 6 ：\(\boxed{-\frac{1}{2}}\)

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