Chapter 4.1, Problem 30E

a.

To determine

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

Answer to Problem 30E

The co-terminal angles are ${480}^{°}$ and $-{240}^{°}$ .

Explanation of Solution

Given:

The given angle is ${120}^{°}$ .

Calculation:

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

Now

  ${120}^{°}+{360}^{°}={480}^{°}$ (positive)

  ${120}^{°}-{360}^{°}=-{240}^{°}$ (negative)

Hence the co-terminal angles are ${480}^{°}$ and $-{240}^{°}$ .

b.

To determine

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

Answer to Problem 30E

The co-terminal angles are ${300}^{°}$ and $-{780}^{°}$ .

Explanation of Solution

Given:

The given angle is $-{420}^{°}$ .

Calculation:

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

Now

  $-{420}^{°}+2\times {360}^{°}=-{420}^{°}+{720}^{°}={300}^{°}$ (positive)

  $-{420}^{°}-{360}^{°}=-{780}^{°}$ (negative)

Draw a figure for the coterminal angles.

Hence the co-terminal angles are ${300}^{°}$ and $-{780}^{°}$ .