Definition:Cotangent

Trigonometry

 * SineCosine.png

In the above right triangle, we are concerned about the angle $$\theta$$.

The cotangent of $$\angle \theta$$ is defined as being $$\frac {\text{Adjacent}} {\text{Opposite}}$$.

Thus it is seen that the cotangent is the reciprocal of the tangent.

It is also seen to be the cosine over the sine.

Real Function
Let $$x \in \R$$ be a real number.

The real function $$\cot x$$ is defined as:


 * $$\cot x = \frac {\cos x} {\sin x} = \frac 1 {\tan x}$$

where:
 * $$\sin x$$ is the sine of $$x$$;
 * $$\cos x$$ is the cosine of $$x$$;
 * $$\tan x$$ is the tangent of $$x$$.

The definition is valid for all $$x \in \R$$ such that $$\sin x \ne 0$$.

Complex Function
Let $$z \in \C$$ be a complex number.

The complex function $$\cot z$$ is defined as:


 * $$\cot z = \frac {\cos z} {\sin z} = \frac 1 {\tan z}$$

where:
 * $$\sin z$$ is the sine of $$z$$;
 * $$\cos z$$ is the cosine of $$z$$;
 * $$\tan z$$ is the tangent of $$z$$.

The definition is valid for all $$z \in \C$$ such that $$\cos z \ne 0$$.

Also see

 * Sine, cosine, tangent, secant and cosecant.