Radians and Degrees

An angle is in standard position if the initial side of the angle is on the x-axis between the 1st and 4th quarter.

An angle that extends counterclockwise¹⁾.

An angle that extends clockwise.

Equivalent angle that has a different numerical value. Add or subtract $360$ for degrees and $2\pi$ for radians to get a coterminal angle.

Degrees is an angle measurement where one full revolution is 360.

Instead of a decimal representation, degrees can also be specified in minutes and seconds, akin to standard time²⁾. The conversion to decimal is $x + \frac{y}{60} + \frac{z}{3600}$ where x is whole unit degrees, y is minutes³⁾, and z is seconds⁴⁾.

A radian is a measurable length where the radius of a circle equals to an arc length section of the circle. $r = s$ where $r$ is the radius and $s$ is the arc length segment.

The conversion is $\pi = 180$ degrees. Degree to Radian: $d * \frac{\pi}{180} = r$ Radian to Degree: $r * \frac{180}{\pi} = d$

• Angles are complementary when they sum up to 90° or $\frac{\pi}{2}$
• Angles are supplementary when they sum up to 180° or $\pi$