Question

Determine the amplitude, period, and phase shift for y=1/3tan (0 +30) and use them to plot the graph of the function.

Answer 1

Given: The function below

$y=\frac{1}{3}tan(\theta+30^0)$

To Determine: The amplitude, the period, and the phase shift

Solution

The graph of the function is as shown below

The general equation of a tangent function is

$f(x)=Atan(Bx+C)+D$

Where

$\begin{gathered} A=Amplitude \\ Period=\frac{\pi}{B} \\ Phase-shift=-\frac{C}{B} \\ Vertical-shift=D \end{gathered}$

Let us compare the general form to the given

$\begin{gathered} y=\frac{1}{3}tan(\theta+30^0) \\ f(x)=Atan(B\theta+C)+D \\ A=\frac{1}{3} \\ B=1 \\ C=30^0 \\ D=0 \end{gathered}$

Therefore

$\begin{gathered} Amplitude=\frac{1}{3} \\ Period=\frac{\pi}{B}=\frac{180^0}{1}=180^0 \\ Phase-shift=-\frac{C}{B}=-\frac{30^0}{1}=-30^0 \end{gathered}$

Hence, the correct option is as shown below