Converting Degrees to Radians

Pre-Calculus · Axiom Academy

EXAMPLE Converting Degrees to Radians Multiply each degree measure by , then reduce the fraction to lowest terms. Convert each of these angles from degrees to radians: , , , and . Every conversion uses the same idea — multiply by the factor (which equals 1 , since radians) and simplify. Nice work. Every degree-to-radian conversion is the same one move: multiply by and reduce. One conversion factor: equals 1 because radians, so multiplying by it changes the units without changing the angle. The work is just fraction reduction: divide the degree measure and 180 by their greatest common divisor. Keep in the answer: a radian measure is normally left exact, as a multiple of , not a decimal. Once you trust the factor, converting any angle is a one-line calculation.

This is the written version of the interactive lesson above. See the full Pre-Calculus course.