One rotation around a circle is 360 degrees or 2pi
radians.
Trigonometric functions such as sine and cosine will "wrap around" when they reach 360 degrees and act the same way as being at 0 degrees. Basically, the following occurs:
angle_in_unit_circle = angle mod 360
Also, some trigonometric functions such as tangent are not defined at certain angles, such as 90 and 270 degrees, where tangent of an angle will return a positive or negative infinity.
This "wrapping" around can be seen by representing the sine, cosine, tangent functions using an right triangle inscribed in an unit circle, and this behavior makes those functions periodic because they will repeat their patterns over and over again.
Wikipedia has an extensive article on Trigonometric functions, so that might be worth taking a look at.
Usage
In terms of use, I can't quite think of a good example off the top of my head, except, maybe perhaps to represent a location of a particle at a certain time in a polar coordinate system, where the angle θ
is dependent on time t
:
r(θ(t)) = t where θ(t) = t
for values of t from 0 to 720, which could then be represented in a Cartesian coordinate system as:
x(t) = r sin(θ(t)) == t sin(t)
y(t) = r cos(θ(t)) == t cos(t)
The particle will be moving in a spiral type movement, dependent on the time t
. In this case, the sine and cosine of angles beyond 360 will be calculated.
(And my math is rusty, so if there are any errors in the equations above, please let me know!)