Chapter four part Bexamines graphsof the sixtrigonometric 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 criticalthat 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 MathResourceCenter in room C117 for extra help.
1.4.5Graphs of Sine and Cosine
Pg. 294-295Odd # 1-15, 23, 27, 31, 35, 41, 43, 45, 49
2.4.5Pg 294-295# 14, 20, 26, 47, 50, 51, 53
3.4.5Pg. 295-7# 55-59all (sketch phase shifts without a calculator)
63-69all, 73, 77
4.4.6Graphs of Other Trig Functions
Pg. 305# 2, 3, 5, 7, 8, 9, 19, 20, 27, 30
5.4.6Pg. 305# 1, 4, 6, 13, 15, 16, 17, 25(be careful!), 26, 41, 43
6.4.7Inverse Trig Functions
Pg. 316# 1-7 all, 11, 12, 13-24 all, 27, 29, 31, 32
7.4.7Worksheet, exact values of inverse trig problems
8.4.7Pg. 317-318# 33-35, 37, 39, 41, 43, 49, 53, 57, 73
9.4.8Applications and Models
Pg. 326#6, 9, 11, 15, 17, 18, 22, 23, 25, 26 & worksheet on 9 trig graphs -- domain/range
10.4.8Pg. 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
Dec3-7 / #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 / #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:
20. g is f moved down 6 units
26. g is f moved two units up
Section 4-6 Pg 305:
2. d
4. f
6. b
Section 4-7 Pg 316:
2a.
2b.
4a.
4b.
6a.
6b.
12.
14. .59
16. 2.35
18. -1.52
20. 1.36
22. -.13
24. 1.40
32. 35
Exact Inverse Values Worksheet:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13. 0
14.
15. undefined
16.
17.
18. 0
19. 0
20.
21.
22.
23.
24.
25. 0
26.
27.
28.
29.
30.
31.
32. 0
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.
166. 1221 miles at N 85.6º E
Chapter Review Sheet:
6.
7.
8. undefined
9.
10. 1
11. .3
12. 0
13.
14.
15.
16.
17. 72.27 ft
18. 109.9 ft
Inverse Trig Functions & Name______
Composite Trig Functions Worksheet
Directions: Write the exact trigonometric value of the following problems.
1.2.3.
4.5.6.
7.8.9.
10.11.12.
13.14.15.
16.17.18.
19.20.21.
22.23.24.
25.26.27.
28.29.30.
31.32.
Pre-Calculus Names______
Graphs of trig functions
Directions: Please show at least one full period with each graph.
1. Graph 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 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 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 below and label.What is the Domain?______
What is the Range?______
5. Graph below and label.What is the Domain?______
What is the Range?______
6. Graph below and label.What is the Domain?______
What is the Range?______
7. Graph below and label.What is the Domain?______
What is the Range?______
8. Graph below and label.What is the Domain?______
What is the Range?______
9. Graph 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
4.Sketch the graph of
5.Sketch the graph of
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.
6.7.
8.arcsin 29.arctan -1
10.sin(arcsin 1)11.cos(arcos .3)
12.13.
14.15.
Write an algebraic expression for the following:
16.
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. b. c.
2. 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**
a. Sketch b. Sketch
3.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.
- 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. b. c.
6. 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 b. Sketch the graph of
c. Sketch the graph of d. Sketch the graph of
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. b.
c. d.
9.I can use properties of inverse trig functions to evaluate expressions.
a. sin(arcsin 1)b. cos(arcos .3)c.
10.I can find the exact value or an algebraic expression for a trig expression by using the “triangle technique.”
a. b.
c. d.
Section 4.8
11.I can solve right triangles for all missing parts.
a. Given an isosceles triangle with base angles of 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.
12.I can solve real-life trig problems, especially problems involving bearings.
- 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?
- 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?
- 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.
- 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.
Per. / πSec. / π/4
Amp/VS / 3/2
H.S. / π/4 left
V.S. / 3 down
Ref. / none
1b.
Per. / 4πSec. / π
Amp/VS / 4
H.S. / 8π right
V.S. / 3 down
Ref. / Over y=-3
1c.
Per. / 2πSec. / π/2
Amp/VS / 2
H.S. / π/2 right
V.S. / 1 up
Ref. / Over x= π/2
2a. check graph with calculator
Per. / πSec. / π/4
Amp/VS / 3
H.S. / π right
V.S. / None
Ref. / Over x-axis
2b. check graph with calculator
Per. / 4πSec. / π
Amp/VS / 2
H.S. / 2π left
V.S. / 2 down
Ref. / none
3a. answers may vary:
4a. answers may vary:
and at 4am the water 49 feet.
5a.
Per. / πSec. / π/4
Amp/VS / ½
H.S. / π/2 right
V.S. / 2 up
Ref. / None
5b.
Per. / 4πSec. / π
Amp/VS / 2
H.S. / 8π left
V.S. / 1 down
Ref. / Over y = -1
5c.
Per. / πSec. / π/4
Amp/VS / 3
H.S. / π/2 right
V.S. / 2 down
Ref. / Over x= π/2
6a. check graph with calculator
Per. / 4πSec. / π
Amp/VS / 2
H.S. / None
V.S. / 2 down
Ref. / None
6b. check graph with calculator
Per. / π/4Sec. / π/16
Amp/VS / 2
H.S. / None
V.S. / 3 down
Ref. / None
6c. check graph with calculator
Per. / 4πSec. / π
Amp/VS / 1/2
H.S. / None
V.S. / 1/2 down
Ref. / none
6d. check graph with calculator
Per. / πSec. / π/4
Amp/VS / 4
H.S. / π/2 left
V.S. / none
Ref. / none
7a. refer to notes or inside
cover of book
8a.
8b.
8c. undefined
8d.
9a. 1
9b.3
9c. 0
10a.
10b.
10c.
10d.
11a. 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