Find the radian measure of the angle with the given degree measure. Round your answer to three...

Question:

Find the radian measure of the angle with the given degree measure. Round your answer to three decimal places.

{eq}\displaystyle -21 ^\circ {/eq}

Converting the Angle from Degree to Radian:

Usually, the measure of an angle is expressed by two units that are degrees and radians. We have a special formula to relate these units; that is,

$$\ \text{1 degree} = \dfrac{\pi}{180} \ \text{Radian} $$

This formula helps us to convert the unit of the angle from radian to degree or degree to radian.

Answer and Explanation: 1

The given measure of the angle {eq}-21^{\circ}. {/eq}

Convert the given measure of the angle in radian:

$$\begin{align*} \text{Measure of the angle} &= -21^{\circ} \\[0.3cm] &= -21 \times 1^{\circ} \\[0.3cm] &= -21 \times \dfrac{\pi}{180} & \left[ \text{Recall that} \ 1 \ \text{degree} = \dfrac{\pi}{180} \ \text{radian} \right] \\[0.3cm] &= -\dfrac{21 \times \pi}{180} \\[0.3cm] &= -\dfrac{21 \times 3.14159}{180} \\[0.3cm] &= -\dfrac{65.97339}{180} \\[0.3cm] &= -0.36651 \\[0.3cm] \therefore \text{Measure of the angle} &\approx -0.367 \end{align*} $$

Hence, the measure of the angle in radian is {eq}\color{blue}{-0.367 \text{ Rad}}. {/eq}


Learn more about this topic:

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Radians and Degrees: Definition & Examples

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Chapter 30 / Lesson 11
5.3K

Radians and degrees are used to measure and describe angles. Learn the distinction between the two by looking at their definitions and examples as well as the importance of these two in mathematical problems.


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