Pretty simple concept I learned in my Honors Algebra II
, 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.
, if you have the angle θ
, then any coterminal angles to θ
can be expressed as:
θcoterminal = θ + 2πk
is any real integer
). (If you're measuring angles in degrees
instead of radians, then the term would be "360°k
" instead of "2πk
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