Chapter 12.1, Problem 27WE

(a)

To determine

Write the formula for the measures of all angles coterminal with the given angle.

Answer to Problem 27WE

  $520°+n\cdot 360°$

where n is an integer.

Explanation of Solution

Given:

The angle is :

  $520°$

Formula Used:

Two angles in standard position are coterminal if their terminal sides coincide.

So, the measures of all angles coterminal with $\theta$ are:

  $\theta +n\cdot 360°$

where n is an integer.

Calculation:

Given angle : $520°$

So, the formula for the measures of all angles coterminal with the given angle is

  $520°+n\cdot 360°$

where n is an integer.

(b)

To determine

Give two angles , one positive and one negative , that are coterminal with the given angle.

  $520°$

Answer to Problem 27WE

  $160°\text{ and }-200°$

Explanation of Solution

Given:

The angle is :

  $520°$

From part (a), we have ,

The measures of all angles coterminal with $520°$ are:

  $520°+n\cdot 360°$

where n is an integer.

Calculation:

The positive angle coterminal with $520°$ is $520°-360°=160°$

The negative angle coterminal with $520°$ is $520°-2\cdot 360°=520°-720°=-200°$