Trigonometric Functions, calculus homework help

  

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1.) You (safely) bungee jump from a 200-feet tall bridge in your town. Your distance above the
water’s surface depends on the time since you jumped. Sketch a reasonable graph.
For questions 2 – 5, sketch the graph of each function, showing two complete cycles between
Label the x-coordinates of any zeros or asymptotes.
2.) y  cos x
3.) y  tan x
4.) y  sin x
5.) y  csc x
For questions 6 – 8, complete the following for the function:
a.) Sketch two complete cycles of the graph.
b.) What is the period?
c.) What is the amplitude?
d.) How is this graph related to its parent graph y  sin x or y  cos x ?
6.) y  5 sin2x
2, 2 .
x
y  3cos  
2
7.)
8.)
y  2sin  2x   1
9.) Which pair of functions has identical graphs?


y  sin  x  
2


y   cos  x  


y  cos  x  
2


10.) Write the particular equation of this transformed cosine graph. (Hint: Try to find the best point
to center the sinusoidal axis.)
11.) Write the particular equation of this transformed sine graph. Assume that the horizontal shift is
1 unit to the right. (Hint: Try to find the best point to center the sinusoidal axis.)
12.) Write the equation of the transformed graph of tangent with period 4 that has been shifted
vertically up 3 units.
13.) Write the equation of the transformed graph of sine with period  that has been shifted
3
vertically up 3 units and has an amplitude of 4 .
14.) Write the equation of the transformed graph of sine with period  that has been shifted
3
horizontally to the right 3 units, has an amplitude of 4 , and has been flipped across the x-axis.
—————————————————————————————————-
y  3sec  2x 
15.) Graphs of y  sec x and
are shown. Identify each graph, explaining your
reasoning.
Answer:
16.) Describe how the graph of the function
Then, graph two periods of
Answer:
y  1.5sin  4x 
.
y  1.5sin  4x 
is related to the graph of y  sin x .
17.) Describe how the graphs of functions f and g are related:
f  x   2cos  x 
g  x   2cos  2x 
Answer:
18.) For the functions below, state the amplitude, period, phase shift, and vertical translation of the
graph for the sinusoid.


y   sin  x    2
4

(a) Amplitude
(b) Period
(c) Phase shift
(d) Vertical translation
Answer:
19.) For the functions below, state the amplitude, period, phase shift, and vertical translation of the
graph for the sinusoid.
y  2cos  2x 
(a) Amplitude
(b) Period
(c) Phase shift
(d) Vertical translation
Answer:
1 
y  3 tan  x 
 2  is related to the graph of the basic trigonometric function
20.) Explain how the graph of
y  tan x .
Answer:
21.) Determine the period, domain, range, zeros, and asymptotes (if any). Then, sketch the graph of the
1 
y  3 tan  x 
2  .
function
(a) Period
(b) Domain
(c) Range
(d) Zeros
(e) Asymptotes
(f) Graph
Answer:
…
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