Question

State theamplitude, period, vertical shift and phase shift for each. help idenity and create peace amongst the war field in my mind.

Answer 1

The general form of the cosine equation is

$y=AcosB(x-C)+D$

A is the amplitude

B is used to dine the period as period = 2pi/B

C is the phase shift

D is the vertical shift

Since the given equation is

$y=\frac{1}{2}cos(3x-180)-5$

Take from the bracket 3 as a common factor

$y=\frac{1}{2}cos3(x-60)-5$

Compare it with the general form

$\begin{gathered} A=\frac{1}{2} \\ \\ B=3 \\ \\ C=60^{\circ}=\frac{60}{180}\pi=\frac{1}{3}\pi \\ \\ D=-5 \end{gathered}$

The amplitude is 1/2

The period = 2pi/3 = (2/3)pi ======== 120 degrees

The phase shift is (1/3)pi =========== 60 degrees

The vertical shift is -5