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Chapter 6: Problem 35

Find the exact value of the expression. $$\sin \frac{\pi}{12} \cos \frac{\pi}{4}+\cos \frac{\pi}{12} \sin \frac{\pi}{4}$$

Short Answer

Expert verified
\(\sqrt{3}/2\)

Step by step solution

01

Recognize and apply the sine addition formula

The given expression is in the form of the sine addition formula where \(A = \pi/12\) and \(B = \pi/4\). Applying the formula we get \(\sin (\pi/12 + \pi/4)\).
02

Simplify the addition

Simplify the addition in the argument of the sine function. Express all angles in terms of \(\pi\). \(\pi/12 + \pi/4 = \pi/12 + 3\pi/12 = 4\pi/12 = \pi/3\). Thus we get \(\sin (\pi/3)\).
03

Substitute the exact value

From the unit circle, we know that the exact value of \(\sin (\pi/3)\) is \(\sqrt{3}/2\).

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Most popular questions from this chapter

Sketch the graph of the function. (Include two full periods.) $$f(x)=-2 \tan \frac{\pi x}{2}$$

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