Chapter 12, Problem 20SGR

To determine

To find: An angle with positive measure and an angle with a negative measure that are coterminal with each angle.

Answer to Problem 20SGR

Positive angle $=\frac{11\pi }{2}$

Negative angle $=-\frac{\pi }{2}$

Explanation of Solution

Given information:

  $-{65}^0$

To find a positive and a negative coterminal with a given angle,

We can add and subtract ${360}^0$ if the angle measured in degrees or $2\pi$ if the angle is measured in radians.

Given angle is

  $\frac{7\pi }{2}$

Positive angle $=\frac{7\pi }{2}+2\pi$

  $\Rightarrow$ Positive angle $=\frac{7\pi +4\pi }{2}$

  $\Rightarrow$ Positive angle $=\frac{11\pi }{2}$

Negative angle $=\frac{7\pi }{2}-2\pi$

  $\Rightarrow$ Negative angle $=\frac{7\pi -4\pi }{2}$

  $\Rightarrow$ Negative angle $=\frac{3\pi }{2}$

As we are not getting negative term, we need to subtract $2\pi$ until we get negative term.

Therefore,

Negative angle $=\frac{3\pi }{2}-2\pi$

  $\Rightarrow$ Negative angle $=\frac{3\pi -4\pi }{2}$

  $\Rightarrow$ Negative angle $=-\frac{\pi }{2}$

Therefore,

Positive angle $=\frac{11\pi }{2}$

Negative angle $=-\frac{\pi }{2}$