Question

State the amplitude, period, vertical shift and phase shift for each.

Answer 1

Given: A trigonometric function

$y=sin(x-60\degree)-3$

Required: To find out the amplitude, period, vertical shift, and phase shift.

Explanation: The trigonometric function of the form

$y=Asin[B(x+C)]+D\text{ ........\lparen1\rparen}$

has

$\begin{gathered} Amplitude=A \\ Time\text{ }Period=\frac{2\pi}{B} \\ Phase\text{ }Shift=C \\ Vertical\text{ }Shift=D \end{gathered}$

If C is positive shift is towards the left, if C is negative shift is toward the right.

Similarly, if D is positive shift is upwards otherwise for negative D shift is downwards. Now comparing the given function we get the following values

$\begin{gathered} A=1 \\ B=1 \\ C=60\degree \\ D=-3 \end{gathered}$

Hence amplitude A=1. Now for the time period T

$T=2\pi$

The phase shift is C=-60, and the vertical shift is D=-3.

Final Answer: Amplitude=1

Phase shift=-60

Vertical shift=-3

Time period is-

$T=2\pi$