Introduction to Conversion from Degrees to Radians
Trigonometry has been used for over two thousand years to solve many realworld problems, among them surveying, navigating, and problems in engineering. Another important use is analytic—the trigonometric functions and their graphs are important in several mathematics courses. The unit circle is the basis of analytic trigonometry. The unit circle is the circle centered at the origin that has radius 1. See Figure 13.1.
Angles have two sides, the initial side and the terminal side. On the unit circle, the initial side is the positive part of the xaxis. The terminal side is the side that rotates. See Figure 13.2.
These equations help us to convert radian measure to degrees and degree measure to radians. We can convert radians to degrees by multiplying the angle by 180/ π . We can convert degrees to radians by multiplying the angle by π /180.
Examples
 Convert 4π /5 radians to degree measure.

Because we are going from radians to degrees, we will multiply the angle by 180/ π .
 Convert 5π /6 radians to degree measure.
 Convert 48° to radian measure.

Because we are going from degrees to radians, we will multiply the angle by π /180.
 Convert −72° to radian measure.
Practice problems for this concept can be found at: Trigonometry Practice Test.
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