Chapter 12.1, Problem 30WE

(a)

To determine

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

Answer to Problem 30WE

  $-3605°+n\cdot 360°$

where n is an integer.

Explanation of Solution

Given:

The angle is :

  $-3605°$

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 : $-3605°$

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

  $-3605°+n\cdot 360°$

where n is an integer.

(b)

To determine

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

  $-3605°$

Answer to Problem 30WE

  $355°\text{ and }-5°$

Explanation of Solution

Given:

The angle is :

  $-3605°$

From part (a), we have ,

The measures of all angles coterminal with $-3605°$ are:

  $-3605°+n\cdot 360°$

where n is an integer.

Calculation:

The positive angle coterminal with $-3605°$ is $-3605°+11\cdot 360°=-3605°+3960°=355°$

The negative angle coterminal with $-3605°$ is $-3605°+10\cdot 360°=-3605°+3600°=-5°$