Determine the period,phase shift,range,and amplitude of y=3cos(x+2pi/3)-2?

Question

sketch one cycle of the graph of each function.

Answer 1

The function is

The standard form of the sin function is

Where A = amplitude, B = angular frequency

B = 1

Amplitude

Period

Phase shift

The amplitude is 3 and the period is .

The interval is corresponds to one cycle of the graph.

Class interval , a = first value, b = second value and n = number of terms.

When dividing this interval into four equal parts produces the key points.

x

 

Answer 2

continued....

(1) Draw a coordinate plane.

(2) Plot the maximum point , minimum point and intercepts

(3) Connect these point with a  smooth curve.

Compared with the graph of , the graph of  is shifted downward two units.

Observe the graph the maximum point at and minimum point at

Therefore,  range