Convert the angle in degrees to radians. Round to two decimal place. 288^\circ \\ 288^\circ =...

Question:

Convert the angle in degrees to radians. Round to two decimal place.

{eq}\displaystyle 288^\circ \\ 288^\circ = \square \text{ radians } {/eq}

Conversion of Measuring Angle from Degree to Raidan:

The conversion of measurement of an angle from degree to radian is done by the product of the measurement in degree and the quotient of {eq}\pi {/eq} over {eq}180. {/eq} For example,

$$5^{\circ} = 5 \times \dfrac{\pi}{180} \Rightarrow 0.0873 \ \text{radian} $$

Answer and Explanation: 1

  • Let us consider the given angle as {eq}\theta = 288^{\circ} {/eq}


To convert the angle from degrees to radians, we multiply the angle by {eq}\dfrac{\pi}{180} {/eq}, as follows:

$$\begin{align*} \theta &= 288^{\circ} \\[0.3cm] &= 288 \times 1^{\circ} \\[0.3cm] &= 288 \times \dfrac{\pi}{180} & \left[ \because 1^{\circ} = \dfrac{\pi}{180} \ \text{radian} \right] \\[0.3cm] &= \dfrac{288 \pi}{180} \\[0.3cm] &= \dfrac{288 \times 3.14159}{180} \\[0.3cm] &= \dfrac{904.77792}{180} \\[0.3cm] &= 5.02654 \\[0.3cm] \therefore \theta &\approx 5.03 \end{align*} $$

Hence, the angle of measure in radians is {eq}\color{blue}{5.03} {/eq}.


Learn more about this topic:

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Radians and Degrees: Definition & Examples

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Chapter 30 / Lesson 11
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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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