Chapter 4, Problem 5RE

To determine

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

Answer to Problem 5RE

The conversion in of an angle ${450}^0$ degree to radian is $7.854$ .

Explanation of Solution

Given: ${450}^0$

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’s consider the following angle ${450}^0$

Now to covert this angle, into radian measure, here need to multiply the degree with angle $\frac{\pi }{{180}^0}$ .

Or in the words,

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

This implies,

  ${450}^0=450\left(\frac{\pi }{180}\right)$ radians

  $\Rightarrow \frac{5\pi }{2}$

  $\Rightarrow 7.854$ .

Hence,Theconversion in of an angle ${450}^0$ degree to radian is $7.854$ .