Penn Foster Trigonometry exam

Exam: 007696RR - GRAPHS OF TRIG FUNCTIONS

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Questions 1 to 20: Select the best answer to each question. Note that a question and its answers may be split across a page break, so be sure that you have seen the entire question and all the answers before choosing an answer.

1. A water wave has the equation y = 7.0 sin [0.65(x − 35.45t)], where x and y are measured in feet and t is measured in seconds. In miles per hour, what is the phase velocity (speed) of the wave? A. 35.45 mph

B. 24.17 mph

C. 9.67 mph

D. 14.0 mph

2.

A.

B.

C.

D.

3. Which of these standard trigonometric functions has the least period? A. cosine

B. cosecant

C. tangent

D. secant

4.

A. None

B. 1

C. 3

D. Infinitely many

5. Which of these functions has period 7?

A.

B.

C.

D.

6.

A.

B. 6p

C.

D.

7. Which standard trigonometric function is graphed below?

A. Cotangent

B. Secant

C. Tangent

D. Cosecant

8. Which of these statements are true??

(i) The domain of the inverse cosine function (y = cos–1 x) is –1 ≤ x ≤ 1.

(ii) The range of the inverse sine function (y = sin–1 x) is 0 ≤ y ≤ p .

(iii) The range of the inverse tangent function (y = tan–1 x) is –p/2 < y < p/2.

A. (i) and (iii)

B. (i), (ii), and (iii)

C. (ii) and (iii)

D. (i) and (ii)

9. Choose the graph of y = sec x. A.

B.

C.

D.

10. What is the period of the graph?

A. 3.5

B. 3

C. 1.5

D. 7

11. What is the amplitude of this graph?

A. 1.5

B. 2

C. 2.5

D. 5

12.

A. 7

B. 4

C. 10

D. 6

13. Which of the following lists contains only functions with vertical asymptotes in their graphs? A. Cosine, sine, secant, cosecant

B. Sine, tangent, secant, cosecant

C. Tangent, secant, cosecant, cotangent

D. Cosine, sine, tangent, cotangent

14.

A. 3

B.

C.

D.

15. What is the equation for shifting the standard sine curve +2 units horizontally? A. y = sin x − 2 B. y = sin (x − 2)

C. y = sin x + 2

D. y = sin (x + 2)

16. What is the translation point of y = 100 tan (6x) + 4? A. (6, 4)

B. (6, −4) C. (0, 4)

D. (0, −4)

17. What is the equation of a cosine function with amplitude 3, transition point (−1, 1), and period p ? A. y = 3 cos [2(x − 1)] + 1 B. y = p cos [3(x − 1)] − 1 C. y = 3 cos [2(x + 1)] + 1

D. y = 3 cos [p (x + 1)] − 1

18. Choose the equation that most likely matches the graph below.

A. y = cot–1 x

B. y = tan–1 x

C. y = sec–1 x

D. y = csc–1 x

19. cot–1 −0.57735 is approximately A. −0.65. B. 2.09.

C. 2.62.

D. −1.05.

20.

A.

B.

End of exam

C.

D.