Unit 1.5 Graphs of Sine and Cosine Functions

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Unit 1.5 Graphs of Sine and Cosine Functions

1.

Find the period and amplitude.

a.	Period: ; Amplitude:
b.	Period: ; Amplitude:
c.	Period: ; Amplitude:
d.	Period: ; Amplitude:
e.	Period: ; Amplitude:

2.

Find the period and amplitude.

a.	Period: ; Amplitude:
b.	Period: ; Amplitude:
c.	Period: ; Amplitude:
d.	Period: ; Amplitude:
e.	Period: ; Amplitude:

3.

Find the relationship between the graphs of

and

. Consider amplitude, period, and shifts.

a.	The period of is times the period of .
b.	is a reflection of in the -axis.
c.	The period of is times the period of .
d.	is a reflection of in the -axis.
e.	is a shift of units to the right.

4.

is related to a parent function

Describe the sequence of transformations from

to

a.	is obtained by a vertical shrink of , and one cycle of corresponds to the interval .
b.	is obtained by a horizontal shrink of , and one cycle of corresponds to the interval .
c.	is obtained by a horizontal shrink of , and one cycle of corresponds to the interval .
d.	is obtained by a horizontal shrink of , and one cycle of corresponds to the interval .
e.	is obtained by a vertical shrink of , and one cycle of corresponds to the interval .

5.

is related to a parent function

Use function notation to write g in terms of f.

a.
b.
c.
d.
e.

6.

Write an equation for the function that is described by the given characteristics.

A cosine curve with a period of

an amplitude of

, a left phase shift of

and a vertical translation down

unit.

a.
b.
c.
d.
e.

7.

For a person at rest, the velocity

(in liters per second) of airflow during a respiratory cycle (the time from the beginning of one breath to the beginning of the next) is given by

,

where

is the time (in seconds).
(Inhalation occurs when

and exhalation occurs when

)

Find the number of cycles per minute.

a.	cycles/min
b.	cycles/min
c.	cycles/min
d.	cycles/min
e.	cycles/min

8.

Determine the period and amplitude of the following function.

a.
b.
c.
d.
e.

9.

Use a graphing utility to graph the function below. Be sure to include at least two full periods.

a.
b.
c.
d.
e.

10.

Find a, b, and c for the function

such that the graph of

matches the graph below.

a.
b.
c.
d.
e.