Problem

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

Solution

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

From Solvely APP
Source: https://solvelyapp.com/problems/7223/

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