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Graphing Tangent Function

The trigonometric ratios can also be considered as functions of a variable which is the measure of an angle. This angle measure can either be given in degrees or radians . Here, we will use radians.

Since, $\tan \left(x\right)=\frac{\sin \left(x\right)}{\cos \left(x\right)}$ the tangent function is undefined when $\cos \left(x\right)=0$ . Therefore, the tangent function has a vertical asymptote whenever $\cos \left(x\right)=0$ .

Similarly, the tangent and sine functions each have zeros at integer multiples of $\pi$ because $\tan \left(x\right)=0$ when $\sin \left(x\right)=0$ .

The graph of a tangent function $y=\tan \left(x\right)$ is looks like this:

Properties of the Tangent Function, $y=\tan \left(x\right)$ .

Domain : $x\in ℝ,x\ne \frac{\pi }{2}+n\pi$ , where $n$ is an integer.

Range : $\left(-\infty ,\infty \right)$

$y$ -intercept : $\left(0,0\right)$

$x$ -intercept : $n\pi$ , where $n$ is an integer.

Period: $\pi$

Symmetry: origin (odd function)

Amplitude and Period of a Tangent Function

The tangent function does not have an amplitude because it has no maximum or minimum value.

The period of a tangent function, $y=a\tan \left(bx\right)$ , is the distance between any two consecutive vertical asymptotes.

Period = $\frac{\pi }{\left|b\right|}$

Also see Trigonometric Functions .