(1) Trigonometry Test

(1 Trigonometry - Trigonometry I Copyright © 2006 Barry Exam Trigonometry I Standards Test Practice Mabillard 0 www.math40s.com www.math40s.com 1

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Unformatted text preview: Trigonometry I Copyright © 2006, Barry Exam Trigonometry I Standards Test Practice Mabillard. 0 www.math40s.com www.math40s.com 1. The minimum and the maximum of a trigonometric function are shown in the diagram. a) Write a cosine equation for the function b) Determine the value of the y – intercept, correct to three decimal places 2. Convert 11π to degrees 18 Trigonometry I Standards Test Practice Exam 1 www.math40s.com 3. Find the exact value of sinθ if cos θ = 1 , and the terminal arm is in Quadrant I. 7 4. What is the period in the function f ( x ) = 3sin ( 5 x ) − 2 5. Given the point (-3, -4), determine the exact values of cosθ and sinθ 6. The length of arc swept out by an angle θ is 50 cm. If the radius of the circle is 18 cm, determine the measure of θ in radians. Trigonometry I Standards Test Practice Exam 2 www.math40s.com 7. Determine a value for x that would make the function f ( x ) = 3csc x undefined in the domain [0, 2π ) 8. Determine the value of f (10 ) in the function f ( x ) = 4 sin ⎡π ( x − 2 ) ⎤ + 3 ⎣ ⎦ 3π ⎞ ⎛ 9. The graph of y = 6 cos ⎜ x + ⎟ + 1 is illustrated below. 4⎠ ⎝ Determine the exact values of g, h, m & n. Trigonometry I Standards Test Practice Exam 3 www.math40s.com 10. If the measure of the central angle is π 4 , determine the measures of the other two angles within the triangle. 11. Determine the number of radians between the hour hand and the minute hand at 7:00. Trigonometry I Standards Test Practice Exam 4 www.math40s.com ⎛ 7π ⎞ 12. Determine the value of cos ⎜ − ⎟ ⎝ 4⎠ 13. The circle x 2 + y 2 = 1 is drawn below, along with the line y = 3 . 2 Determine the coordinates of the two intersection points. 14. The graph of f ( x ) = 6sin x + d touches the x-axis once (but does not pass through) on the interval 0 ≤ x ≤ 2π . A possible value for d is: Trigonometry I Standards Test Practice Exam 5 www.math40s.com 15. a) Graph y = cos x b) Graph y = cos −1 x c) State the domain of f −1 ( x ) 16. The maximum point on a trigonometric graph is at the point (-4, 6), and the minimum point is at (2, -2). If the graph is of the form y = a cos ⎡b ( x + c ) ⎤ + d , then determine ⎣ ⎦ possible values for each of the parameters. Trigonometry I Standards Test Practice Exam 6 www.math40s.com 17. An angle of 15° is equivalent to _______ radians. (exact value) 5π ⎞ ⎛ 18. The exact value of cos −1 ⎜ cos ⎟ is 6⎠ ⎝ 19. Write the general equation of a vertical asymptote in the graph of y = csc x 20. If csc θ = 2 and tan θ < 0 , determine the value of cos θ Trigonometry I Standards Test Practice Exam 7 www.math40s.com ⎡π ⎤ 21. Given the function f ( x ) = 2sin ⎢ ( x − 2 ) ⎥ ⎣2 ⎦ a) Sketch the graph b) Sketch y = f ( x ) 22. If the coordinates of a point P (θ ) on the unit circle is (a, b), then the coordinates of the point P ⎡θ + 180o ⎤ are ⎣ ⎦ Trigonometry I Standards Test Practice Exam 8 www.math40s.com 23. State the period of the graph of y = csc θ 24. Convert 3π to degrees. Express answer to one decimal place. 5 25. Given the function f ( x ) = tan x ⎛ π π⎞ a) Sketch y = f ( x ) on the domain ⎜ − , ⎟ ⎝ 2 2⎠ b) State the domain of f ( x ) c) Sketch the graph of f −1 ( x ) Trigonometry I Standards Test Practice Exam 9 www.math40s.com 26. A floating ball in a lake goes up and down with the tide. At 1 second, the ball has a minimum height of 5 cm below surface level. At 3 seconds, the ball has a maximum height of 5 cm above surface level. a) Sketch a graph for the first 4 seconds of motion b) Write an equation for the function 27. If the product of cos x and sin x is negative, then which quadrant is the angle in? ⎛1⎞ 28. The value of sin −1 ⎜ ⎟ is ⎝2⎠ π⎞ ⎛ 29. The exact value of sin ⎜ cos ⎟ is 2⎠ ⎝ Trigonometry I Standards Test Practice Exam 10 www.math40s.com ⎛1 3⎞ 30. If the coordinates of a point P (θ ) on the unit circle are ⎜ , − ⎟ , then the ⎜2 2⎟ ⎝ ⎠ o coordinates of the point P ⎡θ + 180 ⎤ are ⎣ ⎦ 31. A tire rolls 3π metres while turning 240°. Determine the area of the wheel. Trigonometry I Standards Test Practice Exam 11 www.math40s.com MULTIPLE CHOICE SECTION 1. Given csc θ = 5 , the exact value of tan θ is 4 5 4 3 b) 5 a) 3 4 4 d) ± 3 c) ± π m. The tire is rolled and travels a total distance of 28π m. 5 By the time the tire stops, it has rolled through an angle of 2. A tire has a radius of a) 28π b) 140° 28 c) rad 5 d) 8021.41° 3. Given the trigonometric function f ( x ) = cos x , the statement which is true is a) f ( x) = − f ( x) b) f ( x) = f ( −x) c) f ( x ) = f −1 ( x ) d) f ( x) = − f (−x) 4. If 900 < θ < 1800 , a true statement is a) 00 < θ < 900 b) cos θ ≤ tan θ c) 0 < sin θ < 1 d) 0 < cos θ < 1 Trigonometry I Standards Test Practice Exam 12 www.math40s.com 5. Given the function f ( x ) = 12 cos ( 2 x ) , and the transformation g ( x ) = then the amplitude of g ( x ) is a) b) c) d) 1 f ( x) , 4 2 3 4 12 6. The function f ( x ) = 2sec x has a range of a) ( −2, 2 ) b) ( −∞, −2] ∪ [2, ∞ ) ⎡ 1 1⎤ c) ⎢ − , ⎥ ⎣ 2 2⎦ d) ( −∞, ∞ ) 7. A wheel turns through an angle of 16 radians. This angle measurement in degrees is a) b) π0 8 180 π c) 8π 0 d) 28000 π 8. A sine function has a range of [-6, 2] and a period of 4. A trigonometric equation with these properties is ⎛π ⎞ a) y = 8 sin ⎜ θ ⎟ + 2 ⎝2 ⎠ b) y = 4sin ( 4θ ) − 2 ⎛π ⎞ c) y = 4 sin ⎜ θ ⎟ − 2 ⎝2 ⎠ ⎛2 ⎞ d) y = 4sin ⎜ θ ⎟ − 2 ⎝π ⎠ Trigonometry I Standards Test Practice Exam 13 www.math40s.com 9. The angle 24π is co-terminal to an angle of 3 a) 0˚ 2π b) 3 5π c) 6 7π d) 3 ⎛ 7π ⎞ 10. The exact value of csc ⎜ ⎟ is ⎝4⎠ a) − 2 2 b) − 2 2 c) 2 2 d) 11. Given that cos θ = a) b) c) d) 4 3 and sin θ = − , then the terminal arm is located in quadrant 5 5 I II III IV 12. The period of the function g(x) is 8. If g ( 0 ) = 12, g ( 4 ) = 6, and g ( 8) = 12 , then the value of g (12 ) is a) b) c) d) 0 6 12 18 Trigonometry I Standards Test Practice Exam 14 www.math40s.com 13. An angle of 3π on the unit circle has coordinates of 2 13 , 22 22 b) − , 22 c) (0, -1) d) (-1, 0) a) 14. If secθ > 0 and sin θ < 0 , then θ terminates in quadrant a) I b) II c) III d) IV 1 π⎞ ⎛ 15. The period and phase shift for the trigonometric equation y = sin 4 ⎜ θ − ⎟ are 2 3⎠ ⎝ π a) period = 4 ; phase shift = left 3 π b) period = 4 ; phase shift = right 3 π π c) period = ; phase shift = left 2 3 π π d) period = ; phase shift = right 2 3 16. The equation of an asymptote on the graph of y = csc x is π a) x = 4 π b) x = 2 c) x = π 3π d) x = 2 Trigonometry I Standards Test Practice Exam 15 www.math40s.com 17. If tan x sin x < 0 , then x terminates in quadrants a) II or III b) II or IV c) I or IV d) III or IV ⎛ 2⎞ 18. The value of sin −1 ⎜ ⎜ 2 ⎟ is: ⎟ ⎝ ⎠ π a) 4 5π b) 4 4π c) 3 11π d) 6 Trigonometry I Standards Test Practice Exam 16 www.math40s.com ...
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This note was uploaded on 02/09/2011 for the course 168 comm 168 taught by Professor Kiscabean during the Winter '10 term at UCLA.

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