Chapter 4.1, Problem 15E

a.

To determine

Find co-terminal (one positive and one negative) angles for the given angle.

Answer to Problem 15E

The co-terminal angles are $-\frac{11\pi }{6}$ and $\frac{13\pi }{6}$ .

Explanation of Solution

Given:

The given angle is $\frac{\pi }{6}$ .

Calculation:

Co-terminal angle $\to$ two angles are co-terminal when they have the same initial and terminal sides.

Now

  $\frac{\pi }{6}+2\pi =\frac{\pi +12\pi }{6}=\frac{13\pi }{6}$ (positive)

  $\frac{\pi }{6}-2\pi =\frac{\pi -12\pi }{6}=-\frac{11\pi }{6}$ (negative)

Draw a figure for the coterminal angles.

  

Hence the co-terminal angles are $-\frac{11\pi }{6}$ and $\frac{13\pi }{6}$ .

b.

To determine

Find co-terminal (one positive and one negative) angles for the given angle.

Answer to Problem 15E

The co-terminal angles are $-\frac{5\pi }{6}$ and $\frac{19\pi }{6}$ .

Explanation of Solution

Given:

The given angle is $\frac{7\pi }{6}$ .

Calculation:

Co-terminal angle $\to$ two angles are co-terminal when they have the same initial and terminal sides.

Now

  $\frac{7\pi }{6}+2\pi =\frac{7\pi +12\pi }{6}=\frac{19\pi }{6}$ (positive)

  $\frac{7\pi }{6}-2\pi =\frac{7\pi -12\pi }{6}=-\frac{5\pi }{6}$ (negative)

Draw a figure for the coterminal angles.

  

Hence the co-terminal angles are $-\frac{5\pi }{6}$ and $\frac{19\pi }{6}$ .