Pretty simple concept I learned in my Honors

Algebra II/

trigonometry, but the term "coterminal

angle" doesn't seem to catch on...

Two angles are coterminal when they are in the same position in the

Cartesian coordinate plane. For example, the angles 0 and 2π (in

radians) are coterminal since they both represent the same position.

Mathematically, if you have the angle

`θ`, then any coterminal angles to

`θ` can be expressed as:

`θ`_{coterminal} = `θ` + 2π`k`

where

`k` is any

real integer (

positive or

negative). (If you're

measuring angles in degrees instead of radians, then the term would be "360°

`k`" instead of "2π

`k`".)

One of the properties (I don't think there are many more...) of coterminal angles is that the value of a

trig function for angles that are coterminal will be the same for

both angles (e.g. since π/6 and 13π/6 are coterminal angles, sin(π/6) = sin(13π/6) = 1/2).

A concept similar to coterminal angles is that of the

reference angle.