Question

1. find the exact value of the expression cos 17π/12

Explanation:

Step1: Rewrite the angle

We know that \(\frac{17\pi}{12}= \frac{9\pi}{12}+\frac{8\pi}{12}=\frac{3\pi}{4}+\frac{2\pi}{3}\). So, \(\cos\frac{17\pi}{12}=\cos(\frac{3\pi}{4}+\frac{2\pi}{3})\).

Step2: Use the cosine addition formula

The cosine addition formula is \(\cos(A + B)=\cos A\cos B-\sin A\sin B\). Here \(A=\frac{3\pi}{4}\), \(B = \frac{2\pi}{3}\).
We know that \(\cos\frac{3\pi}{4}=-\frac{\sqrt{2}}{2}\), \(\sin\frac{3\pi}{4}=\frac{\sqrt{2}}{2}\), \(\cos\frac{2\pi}{3}=-\frac{1}{2}\), \(\sin\frac{2\pi}{3}=\frac{\sqrt{3}}{2}\).
Substitute these values into the formula:

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Answer:

\(\frac{\sqrt{2}-\sqrt{6}}{4}\)