Chapter 4, Problem 11RE

To determine

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

Answer to Problem 11RE

The angle $-3.5$ radian when expressed in degrees is $-200.535$ .

Explanation of Solution

Given: $-3.5$

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 us consider the following angle $-3.5$

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

Or in other words,

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

Now convert it into degree as follows

  $-3.5=-3.5\left(\frac{180}{\pi }\right)$

  $\Rightarrow -200.535$

Hence,the angle $-3.5$ radian when expressed in degrees is $-200.535$ .