Chapter 4, Problem 9RE

To determine

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

Answer to Problem 9RE

The angle $\frac{3\pi }{10}$ radian when expressed in degrees is $54.000$ .

Explanation of Solution

Given: $\frac{3\pi }{10}$

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:

Let consider the following angle $\frac{3\pi }{10}$

Now to convert this angle into degree measure, need to multiply the radian angle $\frac{180}{\pi }$

Or in the other words,

  $\text{1rad=1}\left(\frac{\text{180}}{\text{π}}\right)\text{degrees}$

Now convert it into degree as follows:

  $\frac{3\pi }{10}=\frac{3\pi }{10}\left(\frac{180}{\pi }\right)$

  $\Rightarrow \frac{3\left(180\right)}{\pi }$

  $\Rightarrow 54.000$

Hence, the angle $\frac{3\pi }{10}$ radian when expressed in degrees is $54.000$ .