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Chapter 5: 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

Identify the trigonometric identity

Recognize that the given expression is in the form of the sine of a sum, which is \(\sin(a+b) = \sin a \cos b + \cos a \sin b\). Here, a is \(\frac{\pi}{12}\) and b is \(\frac{\pi}{4}\). So, the given expression can be re-written as \(\sin(\frac{\pi}{12}+\frac{\pi}{4})\).
02

Simplify the expression

Simplify the expression \(\frac{\pi}{12}+\frac{\pi}{4}\) to get \(\frac{4\pi}{48}+\frac{12\pi}{48}\), which equals \(\frac{16\pi}{48}\) or \(\frac{\pi}{3}\). So, the expression from Step 1 is \(\sin(\frac{\pi}{3})\).
03

Find the exact value

Lastly, find the sine of \(\frac{\pi}{3}\). Since \(\frac{\pi}{3}\) is a standard angle, \(\sin(\frac{\pi}{3}) = \sqrt{3}/2\).

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Most popular questions from this chapter

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