Chapter 12.1, Problem 17WE

To determine

To sketch given angle in standard position and then find its measure.

Answer to Problem 17WE

The angle is ${576}^{\circ }$ .

Explanation of Solution

Given information :

To find $1\frac{3}{5}$ of a counterclockwise revolution.

Angle is positive when counterclockwise.

We know that the whole revolution is of ${360}^{\circ }$ .

  $\frac{8}{5}$ of ${360}^{\circ }$ is,

  $\frac{8}{5}\times {360}^{\circ }={576}^{\circ }$

Angles more than ${360}^{\circ }$ can be represented in standard position by subtracting the given angle from $n{360}^{\circ }$ where $n$ is a positive integer. The value of $n$ depends on the given angle, the difference of the given angle and $n{360}^{\circ }$ should not exceed ${360}^{\circ }$

Now we calculate angle,

  ${576}^{\circ }-\left({360}^{\circ }\right)={216}^{\circ }$

Hence the angle on the graph will be ${216}^{\circ }$ counterclockwise.