Convert the angle 480^\circ to radians. Clearly show work.

Question:

Convert the angle {eq}480^\circ {/eq} to radians. Clearly show work.

Conversion is the change we can make from one unit to another. The principal angles unit is degrees; however, we can express them in radians since that is their other unit. To make a conversion from degrees to radians, we perform the following steps:

1. Establish the equivalence relationship between degrees radians.
2. Form a conversion factor where radians are in the numerator and degrees are in the denominator.
3. Multiply the given measure by the conversion factor.
4. Simplify if necessary.
5. Express the final result of the conversion.

Given:

$$480^{\circ}$$

First, we express the conversion factor from degrees to radians:

$$\pi = 180 ^{\circ}$$

Express the conversion factor as a fraction:

$$\dfrac{\pi}{180 ^{\circ}}$$

Now, multiply the given measurement by the conversion factor:

$$480^{\circ}\times \dfrac{\pi}{180 ^{\circ}}$$

Simplifying, we obtain:

$$\dfrac{480\pi}{180}$$

Lastly, divide the numerator and denominator by {eq}60 {/eq}:

$$\dfrac{480\pi \div 60}{180\div 60}$$

Simplifying, we obtain:

$$\boxed{\dfrac{8}{3}\pi }$$

Radians and Degrees: Definition & Examples

from

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.