Chapter 12.2, Problem 39PPS

To determine

Calculate the angle with a positive measure and with a negative measure that are co-terminal with each angle.

Answer to Problem 39PPS

The positive and negative angle will be $\frac{5\pi }{4}$ & $-\frac{11\pi }{4}$ .

Explanation of Solution

Given: It is given in the question that the given angle is $\frac{-3\pi }{4}$ .

Concept Used:

In this, use the concept of angles and it has to be known that a co − terminal angle will be ${360}^{\circ }$ or $2\pi$ .

Calculation: Here, the angle will be $\frac{-3\pi }{4}$ .

Now, add $2\pi$ to the angle to get positive angle,

  $\frac{-3\pi }{4}+2\pi =\frac{-3\pi +8\pi }{4}=\frac{5\pi }{4}$

Now, subtract $-2\pi$ to the angle to get negative angle,

  $\frac{-3\pi }{4}-2\pi =\frac{-3\pi -8\pi }{4}=-\frac{11\pi }{4}$

Conclusion:

The positive and negative angle will be $\frac{5\pi }{4}$ & $-\frac{11\pi }{4}$ .