Trigonometry 1 Review for the District Final

Transcription

1 Review for the District Final Directions: There are 4 multiple-choice questions (1-4). Do not write in this test booklet. Read each question carefully. Fill in the circle (A, B, C, or D) for the best answer on your answer sheet. You may use calculators. Test revision date: 6/10/15 Description: multiple choice test 1-4 Courses: Copyright 011 Phoenix Union High School District. All rights reserved. No part of this document may be reproduced without the express prior written permission of the Phoenix Union High School District PHOENIX UNION HIGH SCHOOL DISTRICT NO North Central Avenue Phoenix, AZ 8501

2 - Formula Sheet Remember: Set the calculator MODE to either RADIAN or DEGREE depending on the problem. Coterminal: A complete rotation of a ray results in an angle measuring 360. By continuing the rotation, angles of measure larger than 360 can be produced. Such angles are called coterminal angles; their measures differ by a multiple of 360. Definition of Trigonometric Functions: y x y sin cos = tan = (x 0) r r x r r x csc (y 0) sec (x 0) cot = (y 0) y x y Cofunction Identities: sin A cos(90 A) sec A csc(90 A) tan A cot(90 A) cos A sin(90 A) csc A sec(90 A) cot A tan(90 A) Arc Length, Area of Sector, and Linear Velocity Formulas: - Page of 1 PUHSD 015

3 - Formula Sheet Arc Length, s: s = rɵ, where s is the arc length, r is the radius, and Ɵ is the central angle in radians. Area of a Sector: 1 A r, in radians. Linear Velocity: r s v, v r, v. in radians. t t Angular Velocity :, in radians. t Circular Function Characteristics: Trigonometric Function Period Domain Range Vertical Asymptote at sin x π (, ) [-1, 1] none cos x π (, ) [-1, 1] none tan x π (, ) x x (n 1), where n is any integer (undefined) cot x π x x n, where n is any integer (, ) sec x π x x (n 1), where n is any integer π (undefined) (, -1] U [1, ) 3,, (undefined) 0,, (undefined) csc x π x x n, where n is any integer (, -1] U [1, ) Identifying Amplitude, Period, Vertical Translation, and Phase Shift: Generic Form: y = c + asinb(x - d) a = amplitude b: period = b c = vertical translation d = phase shift (horizontal translation) - Page 3 of 1 PUHSD 015

4 1. Find the complement of an angle whose measure of18 15' A ' Find the supplement of an angle whose measure of 36 36' A ' Perform the calculation 45 7'51" 3 10'54" A '45" 75 39'46" 76 39'4" 75 39'46" 4. Convert the angle to decimal degrees and round to the nearest hundredths of a degree. 5 4'16" A Give an expression that generates all angles coterminal with 35º 6. A. 35 n n n n 180 Find the measures of two complementary angles with measures (0w + 15)º and (10w). A. 15, 55 65, 5 15, 85 0, Convert to degrees, minutes, and seconds. A Find the angle of smallest possible positive measure coterminal with 15. A PUHSD 015 Page 4 of 1

5 9. Find the values of m and n in the pair of similar triangles. 11. Evaluate sin 90 cos180 5 tan 360. A Determine which of the following is not possible. A. sin α = 3 4 A. n13, m 13 n9, m 6 n6, m 10 n6, m Find the values of sin θ, cos θ, and tan θ for the angle in standard position having 1,5 on its terminal side. cos β = 1 tan 90 csc θ = 13. What is the co-function ofsin35 6'? A. sin34 6' cos15 6' A. 1 sin, 13 5 cos, 1 1 tan sin, cos, tan sin, 13 1 cos, sin, cos, tan 1 5 tan 1 cos54 34' csc54 34' PUHSD 015 Page 5 of 1

6 14. Find sin A, cos A, and tan A for the figure below. For problems 16-18, evaluate the expressions. Give the exact value. Rationalize denominators when applicable. 16. tan 60 0 A A sin A, cos A, tan A sin A, cos A, tan A sin A, cos A, tan A sin A, cos A, tan A sec 495 sin 570 A Solve cos(515 ) sin (43 ) for. Assume that all angles are acute angles. A (sin 30 )(sec135 ) tan 135 A PUHSD 015 Page 6 of 1

7 19. Determine which of the following is true. A. sin 44 sin 6. Solve the following right triangle. The right angle is at sec 65 sec 45 tan 6 tan 41 cos 4 cos 9 0. Find the decimal approximation for tan A Find an angle in the interval 0,90 satisfies the statement cos A that A. a 10.7, b 18.4, C 54.5 a 19.1, c.8, C 54.8 a 14., c 6.3, C 40.5 a 15.1, c 34.5, C A scientist is at a spot that has an angle of elevation of 5.4 to the top of the 3- foot tall observatory. How far is the scientist from the base of the observatory? A. 341ft. 470 ft. 816 ft ft. 4. Which of the following describes the measures of all angles that are coterminal with the angle whose measure is 8 radian? (Assume n is any integer.) A. 8 + n +1 + n 8 n 8 E. None of the above. PUHSD 015 Page 7 of 1

8 5. Convert 70 degree measures to radians. Leave your answers as multiples of π. A Convert None of the above. A radian measures to degrees. 4 None of the above Evaluate sin. Give exact values. 4 1 A Evaluate csc. Give the exact value. 4 A. 0 undefined 7. Convert 5 radian measures to degrees. 8 A Find the length s in the figure below. 15 s 165 None of the above. A PUHSD 015 Page 8 of 1

9 31. What would be the radius of the circle be if the arc length doubled (and the central angle remained unchanged)? 34. Find the linear velocity of a point on the edge of a wheel rotating 40 times per min. The radius of the wheel is 10 cm. A A..5 cm/sec 8.8 cm/sec 41.9 cm/sec 80.4 cm/sec 3. Find the area of a sector of a circle intercepted by a central angle of 35 in a circle of radius 8.8 in. A in 05.3in 13.4in 33.4in 35. Which of the six trigonometric functions has a period of π and has a vertical asymptote at? A. cos x csc x sec x tan x 36. What is the range ofsin x? 33. Find the value of w in the interval 0, such that tan w = 1. A A., 1,1 x n, 1 1, 37. What is the minimum value of y 3sin 6x? A PUHSD 015 Page 9 of 1

10 38. Which of the following is the equation of the sec function with period 6π and a vertical translation up units? A. y 3secx sec 3 x y In problems 41-4, choose the graph that best describes each function. Each graph displays a one-period interval. 41. y 4sin x A. y sec4x y sec x In problems 39-40, for each function, give the amplitude (A), period (P), vertical translation (V), and phase shift (PS), as applicable. 39. y 3 csc x A. P, V 3 down, PS none P, V 3 up, PS none 3 P, V none, PS 3 to the right P, V 3 down, PS to the left 40. y 3 3cos x 4 A. A 4, P, V 4 down, PS none A 1, P, V 4 down, PS to the right 4 A 4, P, V 4 up, PS none A 3, P, V 3 up, PS to the left 4 PUHSD 015 Page 10 of 1

11 4. x y 6cos A. PUHSD 015 Page 11 of 1

12 Answer key: 1. C. C 3. A 4. B 5. A 6. B 7. D 8. D 9. C 10. C 11. A 1. C 13. C 14. C 15. A 16. B 17. A 18. C 19. C 0. C 1. D. A 3. B 4. C 5. C 6. D 7. A 8. D 9. A 30. C 31. D 3. A 33. A 34. C 35. D 36. B 37. A 38. B 39. A 40. D 41. B 4. D PUHSD 015 Page 1 of 1