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:

$y=-2+3\cos(\frac{1}{2}x-\frac{\pi}{3})$

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

Sol:

Graph of function is:

Amplitude is 3

The period of the graph is:

$\begin{gathered} =\frac{14\pi}{3}-\frac{2\pi}{3} \\ \\ =\frac{12\pi}{3} \\ \\ =4\pi \end{gathered}$

The vertical shift is -2.

For horizontal translation is:

$=\frac{2\pi}{3}$