Algebra 2CP
Trig Unit Part II Worksheet Answers
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For each of the five graphs below a) draw one cycle b) find the period c) write the equation of the center line axis
d) find the amplitude e) find the frequency
1. b) period = 3
c) y = 2
d) amplitude = 4
1
e) frequency 
3
4. b) period = 7
c) y = 1.5
d) amplitude = 2.5
1
e) frequency 
7
2. b) period = 4
c) y  2
d) amplitude = 2
1
e) frequency 
4
5. b) period = 4
c) y = 0.5
d) amplitude = 2.5
1
e) frequency 
4
6.
7.
8.
9.
3. b) period = 3
c) y = 2.5
d) amplitude = 2.5
1
e) frequency 
3
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10. For each of the following, find the domain values 0  x  360 for which the graph of
a) y  sin( x) decreases from 1 to 0
b) y  cos( x) decreases from 1 to 0
90  x  180
0  x  90
c) y  sin( x) increases from 1 to 0
d) y  cos( x) increases from 1 to 0
e) y  sin( x) increases from 0 to 1
f) y  cos( x) increases from 0 to 1
g) y  sin( x) decreases from 0 to 1
h) y  cos( x) decreases from 0 to 1
270  x  360
0  x  90
180  x  270
180  x  270
270  x  360
90  x  180
11. Tell whether each of the following statements describes a characteristic of the sine function, the cosine function, both
functions or neither function.
a) The function increases throughout the interval 180  x  360 .
cosine function
b) The domain of the function is all real numbers.
both functions
c) The graph crosses the x-axis at multiples of 180 .
sine function
d) The amplitude of the function is 1 .
neither function
e) The function has a period of 180 .
f) The function passes through (0,1)
neither function
g) The function is increasing on the interval 0  x  90 .
sine function
cosine function
h) The center line axis of the function is y = 0.
both functions
j) The range of the function is 1  y  1 .
i) The maximum value is 1.
both functions
both functions
12. Use the graph of y  sin( x) to estimate the value of each of the following.
a) sin(35)
0.5
b) sin(115)
c) sin(235)
0.8
d) sin(335)
0.9
0.4
13. A vertical gear of an old clock makes one counterclockwise revolution every 60 seconds. Suppose there is a catch on the
side of the gear that is at its rightmost position at the time t  0 and suppose the vertical position of the catch at this time is
called h  0 .
a) If the vertical position of the catch after 5 seconds is h  4 mm , after how many more seconds will it again be at
20 seconds
h  4 mm ?
b) Name two times during the first 60 seconds that its vertical position will be h  4 mm .
35 seconds & 55 seconds
For each of the following find the equation of the center line axis, the period, the amplitude and the phase shift. Draw each
function showing at least one cycle. Label the high, low and center line points of one cycle. Check your answers on the
graphing calculator. REMEMBER: The   axis is the same as the x  axis .
1 
14. y  3sin   
15. y  5sin( )  3
16. y  cos(2 )  1
2 
center line axis: y  0
period: 720
amplitude: 3
phase shift: 0
center line axis: y  3
period: 360
amplitude: 5
phase shift: 0
center line axis: y  1
period: 180
amplitude: 1
phase shift: 0
1

19. y  4sin  (  45) 
2

18. y   sin(2(  60))
17. y  1.4cos(  45)
center line axis: y  0
period: 360
amplitude: 1.4
phase shift: 45
center line axis: y  0
period: 180
amplitude: 1
phase shift: 60
21. y  3cos  4   30    1
20. y  6cos  3   1
center line axis: y  1
period: 120
amplitude: 6
phase shift: 0
center line axis: y  0
period: 720
amplitude: 4
phase shift: 45
22. y  8sin 1.5(  90)  3
center line axis: y  1
period: 90
amplitude: 3
phase shift: 30
Write both a sine equation and a cosine equation for each of the following graphs.
(210, 1) (150,1)
(15, 4)
23.
24.
center line axis: y  3
period: 240
amplitude: 8
phase shift: 90
(20,1) (40, 4)
25.
(160, 4)
(60,1)
(30,1)
(120, 1)
 60, 1
(30, 3)
(105, 2)
y  2sin( x  60)  1
y  2cos( x  150)  1
(100, 9 )
y  3sin(2( x  30))  1 y  5sin(1.5( x  160))  4
y  3cos(2( x  15)  1 y  5cos(1.5( x  20))  4
Write an equation for each of the following. Graph each equation.
26. a sine function with amplitude 3, period 120 , translated 3 units down and translated 50 to the left
y  3sin(3( x  50))  3
27. a cosine function, reflected over its center line axis with amplitude 7.5, period 450 , translated vertically 5 units and
horizontally 20
4

y  7.5cos   x  20    5
5

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Your height above the ground (in feet) on a Ferris wheel with a radius 20 feet and loading platform 5 feet above the ground can
be modeled by the equation h(t )  20cos(9t )  25 where t is measured in seconds and h is measured in feet.
40 seconds
How many revolutions does the Ferris wheel make in 1 minute? 1.5 revolutions
How many feet above the ground are you a) 15 seconds after the Ferris wheel starts?
39 ft
b) 40 seconds after the Ferris wheel starts? 5 ft c) 60 seconds after the Ferris wheel starts? 45 ft
28. How long does it take for the Ferris wheel to make one complete revolution?
29.
30.
31. Graph the equation.
0 seconds, 40 seconds, 80 seconds, . . .
20 seconds, 60 seconds, 100 seconds, . . .
32. At what times will you be at the point closest to the ground?
highest above the ground?
For each of the following, write a new equation, based on the changes made to the properties of the Ferris wheel.
h(t )  20cos(9t )  28
The Ferris wheel makes one revolution in 36 seconds. h(t )  20cos(10t )  25
The radius of the Ferris wheel is 30 feet. h(t )  30cos(9t )  35
33. The Ferris wheel’s loading platform is 8 feet off the ground.
34.
35.
The table below gives the monthly mean temperatures in the Dallas-Ft. Worth area.
Jan
43
Feb
48
March
57
April
66
May
73
June
81
July
85
Aug
85
Sept
77
Oct
67
Nov
56
Dec
47
36. Draw a scatter plot of the data using 1 for January, 2 for February, 3 for March and so on.
37. Assume the following facts: (1) The lowest temperature occurs in January. (2) The highest temperature occurs in July.
(3) The graph is periodic with a period of 12. Model the data with
a) a sine function
b) a cosine function
y  21sin(30( x  4))  64
y  21cos(30( x  1))  64