Chapter 4, Problem 7RE

To determine

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

Answer to Problem 7RE

The conversion in of an angle $-{33}^{0}45^{\prime }$ degree to radian is $-0.589$ .

Explanation of Solution

Given: $-{33}^{0}45^{\prime }$

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 $-{33}^{0}45^{\prime }$

Now to convert this angle, into radian measure, it needs to multiply the degree angle with $\frac{\pi }{{180}^0}$ .

Or in other words,

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

Firstly, write the above angle in complete degree form

  $-{33}^{0}45^{\prime }=-\left(33+\frac{45}{60}\right)$

  $\Rightarrow -33.75$

Now convert into radians as follows

  $-33.75=-33.75\left(\frac{\pi }{180}\right)$

  $\Rightarrow -0.589$ .

Hence, the conversion in of an angle $-{33}^{0}45^{\prime }$ degree to radian is $-0.589$ .