Chapter 13, Problem 6MCQ

Solution

To write: The equivalent radian measure for an angle of $36°$ . Express the answer in terms of $\pi$ and as a decimal rounded to nearest hundredth.

The radian measure of $36°$ is $\frac{\pi }{5}\text{ radians or }0.63\text{ radians}$ .

Given:

The angle is $36°$ .

Concept used:

Multiply the given angle by $\frac{\pi }{180°}\text{ radians}$ to find the radian measure of given angle.

Calculation:

In order to convert an angle of $36°$ to radians measure multiply the angle by $\frac{\pi }{180°}\text{ radians}$ . Therefore, radian measure of $36°$ is evaluated as:

  $\begin{array}{c}36°=36°\cdot \frac{\pi }{180°}\text{ radians}\mathrm{....}\left(\text{Multiply by }\frac{\pi }{180°}\text{ radians}\right)\\ =\frac{\pi }{5}\text{ radians}\mathrm{....}\left(\text{In terms of }\pi \right)\\ \approx 0.63\text{ radians}\mathrm{....}\left(\begin{array}{l}\text{In terms of hundredth }\\ \text{ decimal equivalent}\end{array}\right)\end{array}$

Conclusion:

The radian measure of $36°$ is $\frac{\pi }{5}\text{ radians or }0.63\text{ radians}$ .