Chapter 6.4, Problem 4QR

Solution

To find: The positive and a negative angle coterminal with the given angle.

The positive and a negative angle coterminal are $\frac{7\pi }{3}$ and $-\frac{5\pi }{3}$, respectively.

Given data:

The given angle is $\frac{\pi }{3}$ .

Formula used:

Add or subtract multiples of $2\pi$ (if it is in radians) or multiples of $360°$ (if it is in degrees) to find a coterminal angle.

Calculation:

Find the possible positive coterminal angle.

  $\begin{array}{c}\frac{\pi }{3}+2\pi =\frac{\pi +6\pi }{3}\\ =\frac{7\pi }{3}\end{array}$

Find the possible negative coterminal angle.

  $\begin{array}{c}\frac{\pi }{3}-2\pi =\frac{\pi -6\pi }{3}\\ =-\frac{5\pi }{3}\end{array}$

Therefore, the positive and a negative angle coterminal are $\frac{7\pi }{3}$ and $-\frac{5\pi }{3}$, respectively.