Pre-Calculus Name: ______________________________

4.5 Graphing Other Trigonometric Functions

LEQ:

Example #1- Graph Horizontal Dilations of the Tangent Function

Locate the vertical asymptotes, and sketch the graph of 3

tanx

y .

Guided Practice-Example #1

A. Locate the vertical asymptotes of xy 4tan .

B. Sketch the graph of xy 4tan .

Example #2- Graph Reflections and Translations of the Tangent Function.

A. Locate the vertical asymptotes, and sketch the graph of 4

tanx

y .

B. Locate the vertical asymptotes, and sketch the graph of

2tan

xy .

Guided Practice- Example #2

Locate the vertical asymptotes of the graph of )3tan( xy .

Example #3- Sketch the Graph of a Cotangent Function

Locate the vertical asymptotes, and sketch the graph of xy 2cot .

Guided Practice- Example #3

A. Locate the vertical asymptotes of xy 2cot2

1 .

B. Sketch the graph of xy 2cot2

1 .

Example #4- Sketch Graphs of Cosecant and Secant Functions

A. Locate the vertical asymptotes, and sketch the graph of xy 2sec .

B. Locate the vertical asymtotes, and sketch the graph of

3csc

xy .

Guided Practice- Example #4

A. Locate the vertical asymptotes of

2csc

xy .

B. Sketch the graph of

2csc

xy .

Example #5- Sketch Damped Trigonometric Functions

A. Identify the damping factor f(x) of xx

y sin2

. Then use a graphing calculator to sketch the

graphs of f(x), -f(x), and the given function in the same viewing window. Describe the behavior

of the graph.

B. Identify the damping factor f(x) of xxy 3cos2 . Then use a graphing calculator to sketch the

graphs of f(x), -f(x), and the given function in the same viewing window. Describe the behavior

of the graph.

Guided Practice- Example #5

Identify the damping factor f(x) of xxy sin4 .

A. A guitar string is plucked at a distance of 0.95 centimeter above its rest position, then

released, causing a vibration. The damping constant for the string is 1.3, and the note produced

has a frequency of 200 cycles per second. Write the trigonometric function that models the

motion of the string.

B. A guitar string is plucked at a distance of 0.95 centimeter above its rest position, then

released, causing a vibration. The damping constant for the string is 1.3, and the note produced

has frequency of 200 cycles per second. Determine the amount of time t that it takes the

string to be damped so that 38.038.0 y .

Guided Practice- Example #6

Suppose another string on the guitar was plucked 0.3 centimeter above its rest position with a

frequency of 64 cycles per second and a damping constant of 1.4. Write a trigonometric

function that models the motion of the string y as a function of time t.