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Trigonometry/Pre-Calculus Answer Sheet Ch 6 Test

Graphs of Trigonometric Functions

This is your answer sheet. You may tear it off to do your test. You may write on your test, but all answers need to be marked on this sheet. After you finish the multiple choice portion, be sure to complete the short answer questions on the reverse side of this sheet!!!

Please make sure your letters are clear or they may be counted wrong!! (3 points each)

1. _____ 18. _____

2. _____ 19. _____

3. _____ 20. _____

4. _____ 21. _____

5. _____ 22. _____

6. _____ 23. _____

7. _____ 24. _____

8. _____ 25. _____

9. _____ 26. _____

10. _____ 27. _____

11. _____ 28. _____

12. _____ 29. _____

13. _____ 30. _____

14. _____ 31. _____

15. _____ 32. _____

16. _____ 33. _____

17. _____ 34. _____

Turn over to complete Short Answer Questions (

Short Answer Questions: Show ALL WORK and LABEL all diagrams as you answer the following:

Meteorology: The following table gives the average temperatures for the city of Payson, Arizona for several days in the month of June.

|Day |0 |

| | (A) (B) |

| |[pic] [pic] |

| | |

|17. y = sec(x) |(C) (D) |

| |[pic] [pic] |

|18. y = sin(x) | |

| |(E) (F) |

|19. y = tan(x) |[pic] [pic] |

| | |

|20. y = csc(x) | |

21. Suppose that n is any integer (that is, n = -2, -1, 0, 1, 2…), what is the value of tan(nπ). [Hint: Look at the graph of y = sin(x).]

(A) -1 (B) 1 (C) 1 (D) 0 (E) undefined

2

22. Suppose that n is any odd integer (that is, n = -3, -1, 1, 3…), what is the value of cos(½ nπ). [Hint: Look at the graph of y = cos(x).]

(A) -1 (B) 1 (C) 1 (D) 0 (E) undefined

2

Use the graph shown below to answer the next several questions.

23.What is the AMPLITUDE of the graph shown?

A) 15

B) 7.5

C) 30

D) 60

24.What is the PERIOD of the graph shown?

A) 15

B) 7.5

C) 30

D) 60

25.What is the FREQUENCY of the graph shown?

A) 0.016

B) 0.066

C) 0.133

D) 0.033

26.What is the VERTICAL SHIFT of the graph shown?

A) 12.5

B) 5

C) 20

D) 30

27. Which equation best matches the graph shown at the top of the page?

A) y = 7.5 cos[(π/30) x] + 12.5

B) y = 15 sin[(π/60) x] + 5

C) y = 7.5 sin[(π/30) x] + 20

D) y = 15 cos[(π/60) x] + 12.5

28. Which of the following shows a graph of y = 3 sin (2π x) ?

5

(A) (B)

[pic] [pic]

(C) (D)

[pic][pic]

In the wild, predators such as hawks need prey such as rodents to survive. The population of the rodents and the hawks are cyclic. Suppose the population of rodents and hawks are given as shown in the graphs:

29. Look at the times when the rodent population is at a MAXIMUM. What is happening to the hawks at these times?

(A) The amount of hawks is at a maximum.

(B) The amount of hawks is at a minimum.

(C) The amount of hawks is increasing.

(D) The amount of hawks is decreasing.

30. Look at the times when the hawk population is at a MAXIMUM. What is happening to the rodents at these times?

(A) The amount of rodents at a maximum.

(B) The amount of rodents is at a minimum.

(C) The amount of rodents is increasing.

(D) The amount of rodents is decreasing.

31. Which of the following statements is TRUE?

(A) The rodent population cycles between 900 and 1500 in a 2 year time period.

(B) The rodent population has a larger amplitude than the hawk population.

(C) Both the rodent and hawk population have a period of 10 years.

(D) The hawk population cycles between 900 and 1500 in a 4 year time period.

The object pictured at right is bouncing between position A and position C. The block takes 8 seconds to complete one whole bounce.

32. Assume the block STARTS bouncing (time 0) from position B and it is heading towards C. Which graph below will match the height vs. time of the block as it bounces?

(A) (B)

[pic] [pic]

(C) (D)

[pic] [pic]

33. Which of the following list the correct amplitude, period, and vertical shift for the bouncing block?

(A) amplitude: 2 ft (B) amplitude: 4 ft

period: 4 sec period: 8 sec

vertical shift: 0 ft vertical shift: 4 ft

(C) amplitude: 2 ft (D) amplitude: 4 ft

period: 8 sec period: 4 sec

vertical shift: 2 ft vertical shift: 8 ft

34. Which of the following equations would best model the height of the bouncing block at any time?

(A) y = 2sin[(π/4)t] + 2 (B) y = 4cos[(π/8)t] + 4

(C) y = 2sin[8t] + 4 (D) y = -4sin[(π/2)t] + 0

NOW TURN YOUR ANSWER SHEET OVER TO COMPLETE THE SHORT ANSWER QUESTIONS ON THE REVERSE SIDE!!!

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