Question

Find one angle with positive measure and one angle with negative measure conterminal with the angle $\frac{\pi }{3}$.

Short answer

The positive conterminal angle is $\frac{7\pi }{3}$.

The negative conterminal angle is $-\frac{5\pi }{3}$.

Step-by-step solution

Step 1. Write down the given information.

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

Step 2. Evaluate one positive and another negative conterminal with the given angle.

The positive and negative conterminal angles for the given angle are evaluated as:

The positive conterminal with the given angle$\frac{\pi }{3}$ is $\frac{\pi }{3}+2\pi =\frac{7\pi }{3}$.

The negative conterminal with the given angle $\frac{\pi }{3}$ is $\frac{\pi }{3}-2\pi =-\frac{5\pi }{3}$.

Step 3. Conclusion.

The positive conterminal with the given angle $\frac{\pi }{3}$ is$\frac{7\pi }{3}$.

The negative conterminal with the given angle $\frac{\pi }{3}$ is $-\frac{5\pi }{3}$.