Definition:Trigonometric Function
Definition
The trigonometric functions are real functions originally defined as the ratios of the lengths of the sides of right triangles with a given internal angle.
There are six basic trigonometric functions:
Sine
In the above right triangle, we are concerned about the angle $\theta$.
The sine of $\angle \theta$ is defined as being $\dfrac {\text {Opposite} } {\text {Hypotenuse} }$.
Cosine
In the above right triangle, we are concerned about the angle $\theta$.
The cosine of $\angle \theta$ is defined as being $\dfrac {\text{Adjacent}} {\text{Hypotenuse}}$.
Tangent
In the above right triangle, we are concerned about the angle $\theta$.
The tangent of $\angle \theta$ is defined as being $\dfrac{\text{Opposite}} {\text{Adjacent}}$.
Cotangent
In the above right triangle, we are concerned about the angle $\theta$.
The cotangent of $\angle \theta$ is defined as being $\dfrac {\text{Adjacent}} {\text{Opposite}}$.
Secant
In the above right triangle, we are concerned about the angle $\theta$.
The secant of $\angle \theta$ is defined as being $\dfrac{\text{Hypotenuse}} {\text{Adjacent}}$.
Cosecant
In the above right triangle, we are concerned about the angle $\theta$.
The cosecant of $\angle \theta$ is defined as being $\dfrac {\text {Hypotenuse}} {\text {Opposite}}$.
Also known as
A trigonometric function is sometimes referred to as a direct trigonometric function so as to distinguish it from an inverse trigonometric function.
Some sources use the terms cyclometric function or circular function.
Some older sources refer to a trigonometric function as a trigonometric ratio.
Also see
- Results about the trigonometric functions can be found here.
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): trigonometric function, circular function or cyclometric function
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): trigonometric function
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): trigonometric function