Question

Identify the amplitude, perlod, vertical and horizontal translation, and phase for the graph. Y=-2+3 cos(1/2x - pi/3)

Answer 1

Given:

The function of graph is:

`y=-2+3\cos((1)/(2)x-(\pi)/(3))`

Find-: Amplitude, Period, Vertical shift, horizontal shift

Sol:

Graph of function is:

Amplitude is 3

The period of the graph is:

`\begin{gathered} =(14\pi)/(3)-(2\pi)/(3) \\ \\ =(12\pi)/(3) \\ \\ =4\pi \end{gathered}`

The vertical shift is -2.

For horizontal translation is:

`=(2\pi)/(3)`