6.4

Amplitude and Period of Sine and Cosine Functions

2

Characteristics of the Graphs of y = sin x and y = cos x

Domain: ____________

Range: ____________

Amplitude: The amplitude of the sine and cosine functions is half the

distance between the maximum and minimum values of the function.

The amplitude of both y= sin x and y = cos x is ______.

Period: The length of the interval needed to complete one cycle.

The period of both y= sin x and y = cos x is ________.

Max min

2 2amplitude

Period

The period of a function is the distance required to complete one full cycle.

kP

2

The period of the functions y = sink and y = cosk is given by:

2 2 2

2

2

32

3

1

1

Examples:

• 1.) Find the amplitude of 4cos(Θ)

• 2.) Find the period of y = cos(Θ/2) and compare its graph to cos(Θ).

• 3.) State the amplitude and period of

y = 1/2sin(4 Θ) then graph the function.

• 4.) Write an equation of the cosine function with amplitude = 9.8 and p = 6π.