Angle measurement: π (PI). Radians. Degrees. Definitions. How To Convert

π (PI). Radians. Degrees. What are they and how to use them? How to convert between them

Definitions: π (PI), Radians, Degrees. Angle measurement. Conversions
π (PI)
Definition: π represents the constant ratio of a circle's circumference (circle's length), C, to its diameter, d (d = 2 × r, where r is the radius of the circle).
π is approximately 3.14159, commonly estimated as the fraction ²²/₇.
π = ^C/_d = ^C/_{(2 × r)}
Angle measurement: π. Radians. Degrees
Radians
Definition: A radian is a standard unit of angle measurement. A radian is equal to the angle formed when the length of the arc of a circle is equal to the radius of the same circle.
There are exactly 2π radians in the circumference (the length) of a circle (any circle).
1 radian is roughly 57.296° (degrees).
An angle of 360° = 2π radians, 180° = π radians, 90° = ^π/₂ radians, 45° = ^π/₄ radians.
Degrees
Definition: Angles are usually measured in degrees (°). A degree is a standard unit of angle measurement.
The angle formed by a complete circle is 360°.
An obtuse angle has a measure between (90° and 180°). A right angle is 90°. An acute angle has a measure between (0° and 90°).
Convert degrees to radians
60° (degrees) to radians
An angle of 360° degrees corresponds to an angle of 2 × π radians, or, simpler, an angle of 180° degrees corresponds to an angle of π radians. Convert the measure of an angle of 60° degrees to radians. Using the simple rule of three:

Convert radians to degrees
1.570797 radians to degrees
An angle of π radians corresponds to an angle of 180° degrees. Convert the measure of an angle of 1,570797 radians to degrees. Using the simple rule of three: