The six trigonometric functions are called sine, cosine,
tangent, cosecant, secant, and cotangent. Their domain
consists of real numbers, but they only have practical purposes when these real
numbers are angle measures.
Consider an angle θ in standard position.
Take a point P anywhere on the terminal side of
the angle. Let P have coordinates (x, y) and
distance d from the origin. The distance d of a
point from the origin is the same as the magnitude
of the vector with the same coordinates:
. The trigonometric functions are as follows:
|sine(θ) = sin(θ) = ||
|cosine(θ) = cos(θ) = ||
|tangent(θ) = tan(θ) = ||
|cosecant(θ) = csc(θ) = ||
|secant(θ) = sec(θ) = ||
|cotangent(θ) = cot(θ) = ||
When a given angle, θ, is the input for a trigonometric function, like
sine, one says, "The sine of θ equals..."
Notice that the following pairs of trigonometric functions are reciprocals of
one another: sine and cosecant, cosine and secant, and tangent and cotangent.
Also, notice that the values of the trigonometric functions can be either
positive or negative because x-coordinates and
y-coordinates can also be either positive or