y= -3cos(2x-pie/2) and y=-4cos(2x-pie/2) Two separate math problems

Question

Determine the amplitude, period, and phase shift of each function. Then graph one period of the function.

Answer 1

The above function is in the form .

, ,

Here .

The amplitude  , stretch .

We have period .

So,

Phase shift

Since the period of a sinusoidal function is .

The solutions of the function are

So, is one cycle of the function.

Now find key points using interval difference .
 

x
y	-3	0	3	0	-3

The graph is

Answer 2

Similarly we can find the amplitude, period and phase shift of the function.

Here , ,

Amplitude

Period

Phase shift .

Since the period of a sinusoidal function is .

The solutions of the function are

So, is one cycle of the function.

Now find key points using interval difference .

x
y	-4	0	4	0	-4

The graph of the function is