Determine the amplitude the period and the phase shift fo th

Determine the amplitude, the period, and the phase shift fo the function.

Solution

From given sinusoid is in the form of

y=acos (bx+c)+d

Then compare with given function, y=3cos (1/2 .x -pi/2)

a=amplitude

b gives period, c is used for shift, d gives vertical shift.

Here, amplitude=3

Period=2 (pi)/b=2 (pi)/1/2=4 (pi)

Phase shift =pi/2 to the right.