Chapter 4, Problem 10RE

To determine

Tofind:the angle measure from radians to degrees and round off to three decimal places.

Answer to Problem 10RE

The angle $-\frac{11\pi }{6}$ radian when expressed in degrees is $-{330}^0$ .

Explanation of Solution

Given: $-\frac{11\pi }{6}$

Concept used:

Trigonometric formula:

  ${\text{πradian=180}}^{\text{0}}$

  $\text{1radian=}\frac{{\text{180}}^{\text{0}}}{\text{π}}$

or

  $1^0=1\left(\frac{\pi }{180}\right)\text{radians}$

Calculation:

Consider the angle $-\frac{11\pi }{6}$

In order to convert $-\frac{11\pi }{6}$ to the corresponding degree measurement,multiply with $\frac{180}{\pi }$

Thus,

  $\frac{-11\pi }{6}=\left(\frac{-11\pi }{6}\right)\left(\frac{180}{\pi }\right)$

  $\Rightarrow -11\times 30$

  $\Rightarrow -{330}^0$

Therefore, the angle $-\frac{11\pi }{6}$ radian when expressed in degrees is $-{330}^0$ .