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:
θcoterminal = θ + 2πk
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.