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Chapter 4: Problem 28

Find a cofunction with the same value as the given expression. $$\cos \frac{3 \pi}{8}$$

Short Answer

Expert verified
The cofunction with the same value as the given expression \(\cos \frac{3 \pi}{8}\) is \( \sin(\frac{\pi}{8})\).

Step by step solution

01

Set Up the Right Side of the Identity

We will set up the right side of our identity. We want \(\frac{\pi}{2} - x = \frac{3 \pi}{8}\).
02

Solve for x

To find x, we solve the equation \(\frac{\pi}{2} - x = \frac{3 \pi}{8}\). Rearranging the terms, we will have \(x = \frac{\pi}{2} - \frac{3 \pi}{8}\). Solving this, we find that \(x = \frac{\pi}{8}\).
03

Substitute x into the sin function

Now that we know our value for x, we substitute it into the sin function. We have \( \sin(x) = \sin(\frac{\pi}{8})\).

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Most popular questions from this chapter

Write the equation for a cosecant function satisfying the given conditions. $$\text { period: } 2 ; \text { range: }(-\infty,-\pi] \cup[\pi, \infty)$$

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