The following formulas can be used to convert between radians and degrees:
Another method for converting between radians and degrees is setting up a proportion to solve for the unknown value.
Example 1: Convert 72° to radians.
Step 1: Plug the given value into the formula.
radians = (π/180) * degrees
= (π/180) * 72
= 72π /180
Step 2: Simplify.
72π/180 = 2π/5
72° = 2π/5 radians
Example 2: Convert -5 radians to degrees.
Step 1: Set up a proportion using x for the unknown degree value. We’ll keep degrees on top and radians on bottom to ensure the ratios are equivalent:
Step 2: Cross multiply and simplify to solve the proportion for x.
2π*x = -1800
πx = -900
x = -900/π = -286.5°
-5 radians =-286.5°
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