Chapter
4B
Pre-Calculus Assignment Guide
Chapter four part B examines graphs of the six trigonometric functions. Just like any other graph, you
must be able to sketch the parent graph of a function and then adjust based on translations or stretch/shrink. It is
critical that you memorize the parent graphs as soon as possible (relative min/max, intercepts, period,
amplitude, asymptotes, etc…). As usual, please don’t put them in the short-term memory! Please ask questions
regularly in class or stop by to see me or go to the Math Resource Center in room C117 for extra help.
1.
4.5
Graphs of Sine and Cosine
Pg. 294-295
Odd # 1-15, 23, 27, 31, 35, 41, 43, 45, 49
2.
4.5
Pg 294-295
# 14, 20, 26, 47, 50, 51, 53
3.
4.5
Pg. 295-7
# 55-59 all (sketch phase shifts without a calculator)
63-69all, 73, 77
4.
4.6
Graphs of Other Trig Functions
Pg. 305
# 2, 3, 5, 7, 8, 9, 19, 20, 27, 30
5.
4.6
Pg. 305
6.
4.7
Inverse Trig Functions
Pg. 316
# 1-7 all, 11, 12, 13-24 all, 27, 29, 31, 32
7.
4.7
Worksheet, exact values of inverse trig problems
8.
4.7
Pg. 317-318
9.
4.8
Applications and Models
Pg. 326
#6, 9, 11, 15, 17, 18, 22, 23, 25, 26 & worksheet on 9 trig graphs -domain/range
10.
4.8
Pg. 327-329
#19, 20, 21, 27, 31, 33, 34, 36, 37, 39
11.
Pg 335-337
#49-52, 83-89 odd, 103, 109, 114 (phase shift!), 125, 128, 137, 139, 145, 147,
148, 157, 159, 165, 166,
12.
Chapter 5 part II Review Sheet
# 1, 4, 6, 13, 15, 16, 17, 25 (be careful!), 26, 41, 43
Dec
3-7
#1
#2
#3
#4
Sine/Cosine Quiz
#5
Dec
10-14
#6
#7
Other Trig
Functions Quiz
#8
#9
4.7 Quiz
Dec
17-21
# 33-35, 37, 39, 41, 43, 49, 53, 57, 73
#10
Review
#11
Review
4B Test Part I
4B Test Part II
Even Answers to Chapter
4B
Section 4-5 Pg 294:
14. Period: 24
Amplitude:
3
4
5.

4
6. 
32.

4

7. 
4

20. g is f moved down 6 units
26. g is f moved two units up
8.
Section 4-6 Pg 305:
2. d
4. f
6. b
10. 
Section 4-7 Pg 316:
2a. 
3
2b. 
4a.
2
3
4
4b.  
4
6a. 2
3
6b. 
4
12.
14.
16.
18.
20.
22.
24.
32.
b1, g
1 2 I
F
G
H 2 , 3 JK
F3 ,  I
G
H2 6 JK
.59
2.35
-1.52
1.36
-.13
1.40
35
Exact Inverse Values Worksheet:

1.
6
2.

4
3. 
4. 

2
0
3

9.
3

6
3
11.
4

12.
2
13. 0

14.
2
15. undefined
1
16.
2
3
17.
2
18. 0
19. 0

20. 
3
3
21.
4

22.
3

23.
6

24.
4
25. 0

26.
4
5
27.
6
15
28.
17
12
29.
13
4
30.
3

31.
6
Section 4-8 Pg 327:
6. a = 25
c = 35
A = 45.58º
B = 44.42º
18. 13.44 meters
20. 30 feet
22. 76.7 feet
26. 1.09º
34. 5.46 kilometers
36. S 27.98º W
Chapter Review Pg 335:
50. 1
52. ½
148 a. 
148 b.

4

3
166. 1221 miles at N 85.6º E
Chapter Review Sheet:

6.
6

7. 
6
8. undefined
9. 

4
10. 1
11. .3
12. 0
3
2
5 61
14.
61
4
15.
5
x 1
16.
x  12  4
17. 72.27 ft
18. 109.9 ft
13.
Inverse Trig Functions &
Composite Trig Functions Worksheet
Name________________________________
Directions: Write the exact trigonometric value of the following problems.
3
2
2.
sin 1
bg
5.
arctan 1
F 2I
G
H2 J
K
8.
tan 1 3
F 3I
G
H3 J
K
11.
bg
1.
cos1
4.
cos1 1
7.
arcsin 
10.
tan 1 
13.
tan 1 0
16.
cos sin 1
F F3 II
G
H2 J
KJ
H G
K
2
2
3.
bg
bg
arcsin 1
bg
tan 1 1
6.
1
2
9.
arccos
arccos 
12.
cos1 0
14.
cot 1 0
15.
cos1 2
17.
sin cos1 
18.
tan sin 1 0
F 2I
G
H2 J
K
F
F 1 IJIJ
G
H2 KK
H G
e j
e j
F
7 II
F
G
G
H
KJ
H 6J
K
21.
cos 1 sin
F
5 II
F
G
G
H
KJ
H 3J
K
24.
tan 1 sin
F
F3 IJIJ
G
H4 KK
HG
27.
cos 1 sin 
F
F5 IJIJ
G
H13KK
H G
30.
tan cos1
20.
sin 1 cos
F
 II
F
G
G
H
KJ
H 6J
K
23.
sin 1 cos
F
F IJIJ
G
H2 KK
HG
26.
sin 1 sin
F
F8 IJIJ
G
H17 KK
H G
29.
sin cos1
32.
tan sin 1 cos
19.
cot cos1 0
22.
cos 1 sin
25.
tan 1 cos
28.
cos sin 1
31.
sin 1 cos sin 1
F F F3 III
G
G
J
H2 J
KJ
H G
KJ
HG
K
F F
 III
F
G
G
G
H
KJ
KJ
H H 2J
K
F
5 II
F
G
G
H
KJ
H 4J
K
F
 II
F
G
G
H
KJ
H 2J
K
F
F IJIJ
G
H3 KK
HG
F
F3IJIJ
G
H5KK
H G
Pre-Calculus
Graphs of trig functions
Names______________________________
Directions: Please show at least one full period with each graph.
1. Graph y  sin 1 x below and label.
What is the Domain?_________________________
What is the Range?___________________________
Describe in words where this function is defined on
unit circle.__________________________________
___________________________________________
Why do we select the range that we do?___________
___________________________________________
___________________________________________
2. Graph y  cos 1 x below and label.
What is the Domain?_________________________
What is the Range?___________________________
Describe in words where this function is defined on
unit circle.__________________________________
___________________________________________
Why do we select the range that we do?___________
___________________________________________
___________________________________________
3. Graph y  tan 1 x below.
What is the Domain?_________________________
What is the Range?___________________________
Describe in words where this function is defined on
unit circle.__________________________________
___________________________________________
Why do we select the range that we do?___________
___________________________________________
___________________________________________
4. Graph y  sin x below and label.
What is the Domain?_________________________
What is the Range?___________________________
5. Graph y  cos x below and label.
What is the Domain?_________________________
What is the Range?___________________________
6. Graph y  tan x below and label.
What is the Domain?_________________________
What is the Range?___________________________
7. Graph y  csc x below and label.
What is the Domain?_________________________
What is the Range?___________________________
8. Graph y  sec x below and label.
What is the Domain?_________________________
What is the Range?___________________________
9. Graph y  cot x below and label.
What is the Domain?_________________________
What is the Range?___________________________
Pre-Calculus review worksheet
Chapter 4 part II
1.
Sketch the 6 trig functions for one full period, label the key points and the asymptotes for each. Also define the domain
and range of each function.
 Sin, Cos should have 5 key points labeled
 Tan, Cot should have 3 key points labeled
 Csc, and Sec should have just one point labeled
2.
Sketch the three inverse functions labeling key points and define the domain and range of each.
3.
Sketch the graph of y  3 sin 2 x  2
4.
Sketch the graph of y  2 tan 4 x
5.
Sketch the graph of y  2 sec
b
g
1
x2
2
Find the exact values of the following. If you cannot find the exact answer from memory or the unit circle, use
substitution and draw a triangle to help you.
6.
arctan
8.
3
3
1
2
7.
arcsin
arcsin 2
9.
arctan -1
10.
sin(arcsin 1)
11.
cos(arcos .3)
12.
arctan tan 
14.
sin arctan
b g
F
G
H
5
6
13.
IJ
K
15.
1I
F
G
H 2J
K
Farcsin 3IJ
cosG
H 5K
sin arccos
Write an algebraic expression for the following:
16.
F
G
H
sec arcsin
IJ
K
2
x 1
Answer the following word problems and draw a picture to help answer the question.
17.
In the parking lot of the school, a line from the ground to the top of the new auditorium makes an angle of elevation of
12 degrees. If I am standing 340 feet from the base of the auditorium, how tall is the auditorium’s wall?
18.
I want to measure the distance across the highway without risking my life by crossing it. I am standing at point A and
want to know how far it is across to point B. The bearing from A to B is N 30 W. I walk 40 feet to another point C on
the same side of the highway and the bearing from C to B is N 50 W.
H-Pre-Calculus
Chapter 4 part 2
Targets
Section 4.5
1.
I can identify the period, section, amplitude, horizontal shift, vertical shift, and any
reflection of a sine or cosine curve.
Identify the period, section, amplitude, horizontal shift, vertical shift and reflection(s) of the following:
a.
2.
y  32 cos  2 x  2   3
b.
y  4cos  12 x  4   3
c.
y  2cos  2  x   1
I can sketch a graph of a sine or cosine function that has been stretched
horizontally/vertically, translated horizontally/vertically, and/or reflected.
**Please remember, Sine & Cosine graphs should have 5 key points labeled on a period**
b
a. Sketch y  3 sin 2 x  2
3.
g
b. Sketch
y  2sin  12 x     2
I can write the equation of the trig graph based on its graph.
a. Find an equation of a sine wave with a peak of 12 and a minimum of 6, starts its cycle at 3π and
completes one full cycle every 4π units.
4.
I can use sine and cosine functions to model real life data.
a. The water level in a city water storage tank oscillates in a simple harmonic motion. The water level
varies depending on the time of day and the corresponding demand of the people. The low point of the
water in the tank, 22 feet, occurs at 8am and 8pm when demand is highest. The high points occur at
2am and 2pm with a water level of 58 feet. Create a sinusoidal function that models the data and use it
to predict the water height at 4pm.
Section 4.6
5.
I can identify the period, section, amplitude, horizontal shift, vertical shift, and any
reflection of a tangent, cotangent, secant, and cosecant curve.
Identify the period, section, amplitude, horizontal shift, vertical shift and reflection(s) of the following:
a.
6.
y  12 tan  x  2   2
b.
y  2sec  12 x  4  1
c.
y  3cot  2  x   2
I can sketch a graph of a tangent, cotangent, secant, and cosecant function that has been
stretched horizontally/vertically, translated horizontally/vertically, and/or reflected.


Tan, Cot should have 3 key points labeled with asymptotes on a period
Csc, and Sec should have just two points labeled on a period along with asymptotes
a. Sketch the graph of y  2 sec
c. Sketch the graph of
1
x2
2
y  12 csc  12 x  
b. Sketch the graph of y  2 tan 4 x  3
1
2
d. Sketch the graph of
y  4cot  x  2 
Section 4.7
7.
I can sketch the 3 inverse trig graphs, label important points and define the domain and
range of each.
a. Sketch the three inverse functions labeling key points and define the domain and range of each.
8.
I can evaluate inverse trig functions from memory or by using my calculator
a. arctan 33
b. arcsin   12 
 
c. arcsin(2)
9.
d.
I can use properties of inverse trig functions to evaluate expressions.
a. sin(arcsin 1)
10.
arctan( 1)
b g
c. arctan tan 
b. cos(arcos .3)
I can find the exact value or an algebraic expression for a trig expression by using the
“triangle technique.”
a. sin  arccos   12  
b. sin  arctan  56  

 
c. cos arcsin  53

d. sec arcsin
 x2 1  
Section 4.8
11.
12.
I can solve right triangles for all missing parts.
a.
Given an isosceles triangle with base angles of 3010' 20" and a height of 12, find the legs and base.
b.
Given a right triangle with legs of 50 and 30, find all missing parts. Round answers to the nearest tenth.
I can solve real-life trig problems, especially problems involving bearings.
a. In the parking lot of the school, a line from the ground to the top of the new auditorium makes an angle of
elevation of 12 degrees. If I am standing 340 feet from the base of the auditorium, how tall is the
auditorium’s wall?
b. An airplane flying at 550 mph has a bearing of 58 degrees. After flying 1.5 hours, how far north and how
far east has the plane traveled from its point of departure?
c.
From City A to City B, a plane flies 600 miles at a bearing of N 40º W. Then, from City B to City C, a
plane flies 775 miles at S 20º W. Find the distance from A to C and the bearing to A to C.
d. I want to measure the distance across the highway without risking my life by crossing it. I am standing at
point A and want to know how far it is across to point B. The bearing from A to B is N 30º W. I walk 40
feet to another point C on the same side of the highway and the bearing from C to B is N 50º W.
H-Pre-Calculus
Chapter 4 part 2
Answers to Targets
1a.
5a.
Per.
Sec.
Amp/VS
H.S.
V.S.
Ref.
π
π/4
3/2
π/4 left
3 down
none
Per.
Sec.
Amp/VS
H.S.
V.S.
Ref.
4π
π
4
8π right
3 down
Over y=-3
Per.
Sec.
Amp/VS
H.S.
V.S.
Ref.
π
π/4
½
π/2 right
2 up
None
1b.
7a. refer to notes or inside
cover of book
5b.
1c.
Per.
Sec.
Amp/VS
H.S.
V.S.
Ref.
2π
π/2
2
π/2 right
1 up
Over x= π/2
2a. check graph with calculator
Per.
π
Sec.
π/4
Amp/VS 3
H.S.
π right
V.S.
None
Ref.
Over x-axis
2b. check graph with calculator
Per.
4π
Sec.
π
Amp/VS 2
H.S.
2π left
V.S.
2 down
Ref.
none
3a. answers may vary:
1
y  3sin ( x  3 )  9
2
4a. answers may vary:
y  18sin

( x  5)  40
6
and at 4am the water 49 feet.
6d. check graph with calculator
Per.
π
Sec.
π/4
Amp/VS 4
H.S.
π/2 left
V.S.
none
Ref.
none
Per.
Sec.
Amp/VS
H.S.
V.S.
Ref.
4π
π
2
8π left
1 down
Over y = -1
Per.
Sec.
Amp/VS
H.S.
V.S.
Ref.
π
π/4
3
π/2 right
2 down
Over x= π/2
5c.
6a. check graph with calculator
Per.
4π
Sec.
π
Amp/VS 2
H.S.
None
V.S.
2 down
Ref.
None
6b. check graph with calculator
Per.
π/4
Sec.
π/16
Amp/VS 2
H.S.
None
V.S.
3 down
Ref.
None
6c. check graph with calculator
Per.
4π
Sec.
π
Amp/VS 1/2
H.S.
None
V.S.
1/2 down
Ref.
none
8a.

6
8c.

6
undefined
8d.

9a.
1
9b.
3
9c.
0
8b.
10a.
10b.
10c.
10d.
11a.


4
3
2
5 61
61
4
5
x 1
x  12  4
23.876
11b. 58.3, 31.0º, 59.0º
12a.
72.27 ft
12b. 437.183 miles north
699.640 miles east
12c.
704.006 miles
bearing S 67.6º W
12d. 109.9 ft