Problem 28 - Precalculus Essentials

Question

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

Step-by-Step Solution

Answer

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

Step 1: Set Up the Right Side of the Identity

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

Step 2: 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 \(x = \frac{\pi}{8}\).

Step 3: Substitute x into the sin function

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