Definition:Trigonometric Function

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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
cosine
tangent
cotangent
secant
cosecant.


Sine

SineCosine.png

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

SineCosine.png

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

SineCosine.png

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

SineCosine.png

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

SineCosine.png

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

SineCosine.png

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