Question

Find the period of tan 2x.

Answer 1

Hint: Tan function is periodic, i.e. its period exists. In order to determine the period of tan 2x we apply the formula for the period of tan function.

Complete step-by-step answer:
Given Data; tan 2x

We make a graph of tan function given by tan x, to get a better idea of intervals of tan x.

An interval of tan x means (as shown in the figure), the domain of one full cycle of tan function written as [a, b] where a is the beginning and b is the ending of the cycle.
And the period of tan x is the distance between any two consecutive asymptotes in the graph of tan function.
We know the formula for the period of a tan function, tan x =${\displaystyle \frac{\text{x}}{\text{coefficient of x}}}$.
Hence the period of tan 2x =${\displaystyle \frac{\text{x}}{2}}$.

Note: In order to solve this type of question the key is to understand the concept of period of a trigonometric function. The period of a function is the horizontal length of one complete cycle of its graph. The period may also be described as the distance from one "peak" (max) to the next "peak" (max). The period of a tangent function, y=a tan (bx), is the distance between any two consecutive vertical asymptotes.