Tangent function is one of the six trigonometric functions. Tangent is abbreviated by tan. Tangent of an angle is described in the context of right triangle like other trigonometric functions. Let us suppose a right triangle as shown in the following figure:

Then, tangent of angle $\theta$ is described by the formula:

Few selected important values of tan $\theta$ are listed below in the table:
 $\theta$ tan $\theta$ 0$^o$ 0 30$^o$ $\frac{1}{\sqrt{3}}$ 45$^o$ 1 60$^o$ $\sqrt{3}$ 90$^o$ $\infty$

## Properties of the Tangent Function

Following are few important properties of tangent function:
• Tangent is a discontinuous function.
• Tangent function is an odd function, since tan (-x) = - tan x.
• It is a periodic function with period $\pi$.
• Domain of tangent function is a set of real numbers except for $n\pi + $$\frac{\pi }{2}, where n is an integer. • Range of tangent function is a set of all real numbers, i.e. (-\infty, \infty). • Tangent function has vertical asymptotes - n\pi +$$\frac{\pi }{2}$, where n is an integer.
• Reciprocal of tan $\theta$ is cot $\theta$.

Few basic formulas related to tangent function
are as follows:

1. $\tan \theta$ = $\frac{\sin \theta }{\cos \theta }$
2. $\tan (A\pm B)$ = $\frac{\tan A\pm \tan B}{1\mp \tan A\tan B}$
3. $\tan 2A$ = $\frac{2\tan A}{1 - \tan^{2}A}$

### Sine Graph

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 Calculator with Sine Cosine and Tangent Equation of a Tangent Line Calculator Formulas for Trigonometric Functions