Pre-Calculus Name: ______________________________ 4.5 Graphing Other Trigonometric Functions LEQ:
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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.
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