What is the period of the function f(x) = \tan(3x)? — ACT

What is the period of the function $f(x) = \tan(3x)$ ?

The period of the function is

\frac{\pi}{3}

The parent function

y = \tan(x)

has a standard period of

\pi

. To find the period of a transformed tangent function of the form

y = \tan(Bx)

, the standard period must be divided by the coefficient of

x

, yielding

\frac{\pi}{|B|}

. Substituting

B = 3

gives

\frac{\pi}{3}

Determine the standard period of the parent function.

The parent function is the tangent function,

y = \tan(x)

, which has a standard period of

\pi

The tangent function completes one full cycle of its graph between

-\frac{\pi}{2}

and

\frac{\pi}{2}

Identify the horizontal compression/stretch coefficient from the given equation.

f(x) = \tan(3x)

, the coefficient of

x

B = 3

This coefficient determines how many cycles occur in a standard interval.

Calculate the period using the formula for the tangent function.

Period =

\frac{\pi}{|B|} = \frac{\pi}{3}

Dividing the standard period of

\pi

by the absolute value of the coefficient

B

gives the compressed period of the transformed function.

The period of a transformed tangent function

y = \tan(Bx)

is given by

\frac{\pi}{|B|}

Question