The radians to degrees formula is used to convert radians to degrees. To convert radians to degrees we need to multiply the radians by 180°/π radians. When we measure angles we use two types of units: degrees and radians, 1 degree is written as 1°. And 1 radian is written as 1 (or) 1c i.e. if there is no unit after the measure of an angle, it means that it is in radians. One rotation in a circle is divided into 360 equal parts and each part is called a degree. One complete counterclockwise rotation in radians is 2π and in degrees, it is 360°. Thus, degree measure and radian measure are related. The formula to convert an angle in radians to degrees is:
Angle in Radians × 180°/π = Angle in Degrees
Derivation of Radians to Degrees Formula
One complete rotation around a circle gives 2π radians which is equivalent to 360°. Therefore, we have 2π radians = 360°. Now, to derive the formula for the conversion of radians to degrees, we will simplify this equation.
2π radians = 360°
π radians = 360°/2
π radians = 180°
1 radian = 180°/π
Hence the angle in degrees is obtained by multiplying the angle in radians by 180°/π. i.e.,
Angle in Radians × 180°/π = Angle in Degrees
Hence, the radians to degrees formula has been derived.
Therefore, to convert radians to degrees, use this formula = Radian measure × (180°/π). The final unit of measure will be (°). 1 rad equals 57.296°.
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