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Chapter 4: Problem 18

Find (if possible) the complement and the supplement of each angle. (a) \(\frac{\pi}{12}\) (b) \(\frac{11 \pi}{12}\)

Short Answer

Expert verified
The complement and supplement of \(\frac{\pi}{12}\) are \(\frac{5 \pi}{12}\) and \(\frac{11 \pi}{12}\) respectively. The complement of \(\frac{11 \pi}{12}\) does not exist, while the supplement is \(\frac{\pi}{12}\).

Step by step solution

01

Finding the Complement and Supplement of \(\frac{\pi}{12}\)

First, you will devise the complement by subtracting \(\frac{\pi}{12}\) from \(\frac{\pi}{2}\) using the formula for finding the complement of an angle. Next, discover the supplement by subtracting \(\frac{\pi}{12}\) from \(\pi\) using the formula for finding the supplement of an angle.
02

Finding the Complement and Supplement of \(\frac{11 \pi}{12}\)

Next, determine the complement by subtracting \(\frac{11 \pi}{12}\) from \(\frac{\pi}{2}\). With this angle being greater than \(\frac{\pi}{2}\), the complement will not exist. Then, calculate the supplement by subtracting \(\frac{11 \pi}{12}\) from \(\pi\).

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