Pre-Calculus Chapter 4

Name:___________________________ Period: _______ Date: ____________

Worksheet ~ Graphing Sine & Cosine #6 Write a sine equation for the graphs below. 1.)

2.)

________________________ Write a cosine equation for the graphs below. 3.)

________________________ 5.)

________________________

4.)

________________________

Graph y = −5 cos(4θ ) from 0 ≤ θ ≤ 2π .

π 2

π

3π 2

2π

Write the equation for the functions with the given information.

3π π , Phase Shift = , Vertical Shift: -25 4 2

6.)

Sine Function: Amplitude = 50, Period =

7.)

Cosine Function: Amplitude = 15, Period =

π 6

, Phase Shift =

π 3

, Vertical Shift:

________________________________

5 3

________________________________

State the amplitude, period, phase shift and vertical shift for the following functions.

10 ⎛ 6 2π ⎞ sin⎜ x + ⎟ −1 3 5 ⎠ ⎝7

8.)

y=−

9.)

⎛x π ⎞ y = 5 cos⎜ + ⎟+2 ⎝ 5 15 ⎠

Amplitude: _________ Period: _________ Phase Shift: _________ Vertical Shift: _________

Amplitude: _________ Period: _________ Phase Shift: _________ Vertical Shift: _________

For the following functions, state the amplitude, period, vertical shift and phase shift. Then sketch the graph.

10.)

π⎞ ⎛1 f ( x) = 2 cos⎜ x + ⎟ − 1 2⎠ ⎝4

11.)

π⎞ ⎛ f ( x) = 3 cos⎜ x − ⎟ 2⎠ ⎝

12.)

⎛x π ⎞ f ( x) = sin ⎜ − ⎟ + 2 ⎝ 3 12 ⎠

Amplitude:

_________

Amplitude:

_________

Amplitude:

_________

Period:

_________

Period:

_________

Period:

_________

Phase Shift: _________

Phase Shift: _________

Phase Shift: _________

Vertical Shift: _________

Vertical Shift: _________

Vertical Shift: _________

Graph:

Graph:

Graph: