Chapter 4.1, Problem 29E

a.

To determine

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

Answer to Problem 29E

The co-terminal angles are ${405}^{°}$ and $-{315}^{°}$ .

Explanation of Solution

Given:

The given angle is ${45}^{°}$ .

Calculation:

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

Now

  ${45}^{°}+{360}^{°}={405}^{°}$ (positive)

  ${45}^{°}-{360}^{°}=-{315}^{°}$ (negative)

Hence the co-terminal angles are ${405}^{°}$ and $-{315}^{°}$ .

b.

To determine

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

Answer to Problem 29E

The co-terminal angles are ${324}^{°}$ and $-{396}^{°}$ .

Explanation of Solution

Given:

The given angle is $-{36}^{°}$ .

Calculation:

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

Now

  $-{36}^{°}+{360}^{°}={324}^{°}$ (positive)

  $-{36}^{°}-{360}^{°}=-{396}^{°}$ (negative)

Draw a figure for the coterminal angles.

Hence the co-terminal angles are ${324}^{°}$ and $-{396}^{°}$ .