Find Amplitude, Period, and Phase Shift tan(4x)

$\tan (4 x)$

Step 1

Use the form $a \tan (b x - c) + d$ to find the variables used to find the amplitude, period, phase shift, and vertical shift.

$a = 1$

$b = 4$

$c = 0$

$d = 0$

Step 2

Since the graph of the function $t a n$ does not have a maximum or minimum value, there can be no value for the amplitude.

Amplitude: None

Step 3

Find the period of $\tan (4 x)$ .

The period of the function can be calculated using $\frac{π}{| b |}$ .

$\frac{π}{| b |}$

Replace $b$ with $4$ in the formula for period.

$\frac{π}{| 4 |}$

The absolute value is the distance between a number and zero. The distance between $0$ and $4$ is $4$ .

$\frac{π}{4}$

Step 4

Find the phase shift using the formula $\frac{c}{b}$ .

The phase shift of the function can be calculated from $\frac{c}{b}$ .

Phase Shift: $\frac{c}{b}$

Replace the values of $c$ and $b$ in the equation for phase shift.

Phase Shift: $\frac{0}{4}$

Divide $0$ by $4$ .

Phase Shift: $0$

Step 5

List the properties of the trigonometric function.

Amplitude: None

Period: $\frac{π}{4}$

Phase Shift: None

Vertical Shift: None

Step 6