Review Test 1. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Transcription

1 Review Test 1 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Convert the angle to a decimal in degrees. Round the answer to two decimal places. 1) 4ʹʹʹ A).9 B).8 C).91 D).9 1) ) 91 ʹ1ʹʹ A) B) C) 91.0 D) 91.4 ) ) 1 1ʹ4ʹʹ A) 1. B) 1. C) 1.9 D) 1.4 ) Convert the angle to D Mʹ Sʹʹ form. Round the answer to the nearest second. 4) 14.9 A) 14 ʹ9ʹʹ B) 14 ʹ4ʹʹ C) 14 ʹ48ʹʹ D) 14 ʹʹʹ 4) ) 18.8 A) 18 49ʹ8ʹʹ B) 18 4ʹ8ʹʹ C) 18 0ʹ1ʹʹ D) 18 49ʹ1ʹʹ ) ) 1.0 A) 1 4ʹʹʹ B) 1 1ʹʹʹ C) 1 ʹ4ʹʹ D) 1 1ʹ48ʹʹ ) If s denotes the length of the arc of a circle of radius r subtended by a central angle θ, find the missing quantity. Round to one decimal place, if necessary. ) r = 1.1 centimeters, θ = 1.8 radians, s =? ) A) 0.9 cm B) 1.9 cm C).9 cm D).9 cm 8) r = 1 feet, s = feet, θ =? 8) A) 1 B) 1 radians C) radians D) 9) s =.8 meters, θ = 1.9 radians, r =? A) 1. m B) 0. m C) 0. m D) 1 m 9) 1

2 Find the length s. Round the answer to three decimal places. 10) 10) s π 4 ft A).8 ft B) 1.1 ft C).14 ft D).4 ft 11) 11) s 0 10 m A) 1.49 m B) 9.4 m C) 1.1 m D) m Solve the problem. 1) For a circle of radius 4 feet, find the arc length s subtended by a central angle of 0. Round to the nearest hundredth. A) 4.19 ft B).99 ft C).09 ft D).8 ft 1) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 1) Salt Lake City, Utah, is due north of Flagstaff, Arizona. Find the distance between Salt Lake City (40 4ʹ north latitude) and Flagstaff ( 1ʹ north latitude). Assume that the radius of the Earth is 90 miles. Round to nearest whole mile. 1) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Convert the angle in degrees to radians. Express the answer as multiple of π. 14) 14) A) π B) π C) π 4 D) π 1) 4 A) π 10 B) 10π C) π 9 D) 4π 11 1)

3 1) 8 A) 9π 0 B) 9π 10 C) 9π 0 D) 9π 90 1) 1) 1) A) π 1 B) π 0 C) π 0 D) π 18 Convert the angle in radians to degrees. 18) - π 1 A) -4 B) - C) - D) - 18) 19) - π 19) A) -90π B) - C) -90 D) 0) 9 π A) 0 B) 40 C) 90π D) 8 0) Convert the angle in degrees to radians. Express the answer in decimal form, rounded to two decimal places. 1) A) 0.9 B) 0.94 C) 0.9 D) 0.9 1) ) - A) -.8 B) -.8 C) -.84 D) -.8 ) Convert the angle in radians to degrees. Express the answer in decimal form, rounded to two decimal places. ) A) 11. B) 0.09 C) D) 0.0 ) 4) A) -0.1 B) 0.04 C) 19. D) ) If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If necessary, round the answer to two decimal places. ) r = feet, A = square feet, θ =? ) A) 1 radians B) 44 radians C).9 radians D) 1.14 radians ) θ = π radians, A = square meters, r =? ) A) 4.9 m B) 1. m C) 4.0 m D) 1.9 m ) r = feet, A = square feet, θ =? A) 4,9.99 B). C),4. D) 11.4 )

4 8) r = 44. centimeters, θ = π 8 radians, A =? 8) A) 1.1 cm B) 8. cm C). cm D) 8. cm Find the area A. Round the answer to three decimal places. 9) 9) π 9 yd A). yd B) 4.41 yd C) 1. yd D) 1.0 yd 0) 0) 0 9 ft A).4 ft B).9 ft C) 11. ft D) 0.8 ft Solve the problem. 1) A circle has a radius of 11 centimeters. Find the area of the sector of the circle formed by an angle of. If necessary, round the answer to two decimal places. A) 8.08 cm B) 11.1 cm C).8 cm D) cm 1) ) An irrigation sprinkler in a field of lettuce sprays water over a distance of feet as it rotates through an angle of 1. What area of the field receives water? If necessary, round the answer to two decimal places. A) 14. ft B) 9.4 ft C).1 ft D) 4.8 ft ) ) An object is traveling around a circle with a radius of 10 centimeters. If in 0 seconds a central angle of 1 radian is swept out, what is the linear speed of the object? ) A) radians/sec B) 1 cm/sec C) 1 radians/sec D) cm/sec 4

5 4) An object is traveling around a circle with a radius of 0 meters. If in 10 seconds a central angle of 1 radian is swept out, what is the linear speed of the object? 4) A) m/sec B) 1 m/sec C) 1 8 m/sec D) 1 4 m/sec ) An object is traveling around a circle with a radius of 10 meters. If in 1 seconds a central angle of radians is swept out, what is the linear speed of the object? ) A) 1 m/sec B) m/sec C) m/sec D) m/sec Find the value of the indicated trigonometric function of the angle θ in the figure. Give an exact answer with a rational denominator. ) ) Find sin θ. A) sin θ = 8 B) sin θ = 8 8 C) sin θ = 8 8 D) sin θ = 8 ) ) 9 Find cos θ. A) cos θ = B) cos θ = 10 C) cos θ = D) cos θ = ) 8) 8 Find tan θ. A) tan θ = 9 8 B) tan θ = 9 9 C) tan θ = D) tan θ = 8

6 9) 9) 9 Find csc θ. A) csc θ = 8 8 B) csc θ = 8 C) csc θ = 8 9 D) csc θ = ) 40) 4 Find sec θ. A) sec θ = B) sec θ = 4 C) sec θ = 4 D) sec θ = 41) 8 41) Find cot θ. A) cot θ = B) cot θ = 8 C) cot θ = D) cot θ = 8 Use identities to find the exact value of the indicated trigonometric function of the acute angle θ. 4) sin θ =, cos θ = Find tan θ. 4) A) B) C) D) 4) sin θ =, cos θ = 1 Find sec θ. 4) A) 4 B) 4 C) D)

7 44) sin θ = 1 4, cos θ = 1 4 Find csc θ. 44) A) 1 B) 4 C) D) 1 1 Use Fundamental Identities to find the exact value of the expression. Do not use a calculator. 4) sin + cos A) -1 B) C) 1 D) 0 4) 4) sec - tan A) 1 B) C) -1 D) 0 4) 4) tan - sin cos A) 0 B) C) 1 D) undefined 4) Use the definition or identities to find the exact value of the indicated trigonometric function of the acute angle θ. 48) sin θ = 4 Find tan θ. 48) A) 4 B) 4 C) D) 4 49) cos θ = Find sec θ. 49) A) 4 B) 4 C) 4 D) 0) tan θ = Find sin θ. 0) A) 1 B) C) D) 1) cot θ = 1 Find sin θ. 1) A) 1 B) 1 C) 1 1 D) 1 1 ) sec θ = Find csc θ. ) A) 4 B) 4 C) D) 4 ) csc θ = Find cos θ. ) A) B) C) D) 1

8 Use Fundamental Identities and/or the Complementary Angle Theorem to find the exact value of the expression. Do not use a calculator. 4) csc 0 - tan 0 4) A) 0 B) 1 C) -1 D) ) cos 0 sin 0 + sin 0 cos 0 A) 0 B) -1 C) D) 1 ) ) If tan θ = 10, find the exact value of cot ( π - θ). ) A) 11 B) 1 10 C) 9 D) 10 Solve the problem. ) Given sin 0 = 1, use trigonometric identities to find the exact value of tan π. ) A) B) C) D) 8) Given csc θ =, use trigonometric identities to find the exact value of sec θ. 8) A) 1 B) 1 C) 4 D) 1 4 9) Given tan θ =, use trigonometric identities to find the exact value of cot (90 - θ). A) B) 1 C) D) 9) Find the exact value. Do not use a calculator. 0) sin π 4 0) A) 1 B) C) - D) 1) csc 4 1) A) B) C) D) ) sin 0 ) A) B) C) D) 1 ) csc π ) A) B) 1 C) D) 8

9 Find the exact value of the expression if θ = 0. Do not use a calculator. 4) f(θ) = tan θ Find f(θ). A) B) C) D) 4) ) f(θ) = sin θ Find f(θ). ) A) B) - C) D) - 1 Find the exact value. Do not use a calculator. ) csc 0 - sin 4 ) A) 4 - B) 4 - C) 4 - D) 4 - ) cot π - cos π ) A) B) - C) - D) - 8) 1 + cot 0 - sec 4 A) 0 B) C) 1 D) 8) 9) sin π - cos π 4 - sin π 9) A) -1 B) 0 C) 1 D) 1 Solve the problem. 0) A boat leaves the entrance of a harbor and travels 8 miles on a bearing of N 19 E. How many miles north and how many miles east from the harbor has the boat traveled? Round to the nearest tenth of a mile. A) miles north and 8. miles east B) 8. miles north and miles east C) 8 miles north and 8 miles east D) 41 miles north and 8. miles east 0) 1) A building 0 feet tall casts a 80 foot long shadow. If a person looks down from the top of the building, what is the measure of the angle between the end of the shadow and the vertical side of the building (to the nearest degree)? (Assume the personʹs eyes are level with the top of the building.) A) 0 B) 19 C) 1 D) 0 1) ) A photographer points a camera at a window in a nearby building forming an angle of 4 with the camera platform. If the camera is m from the building, how high above the platform is the window, to the nearest hundredth of a meter? A). m B) 0.9 m C) 4.8 m D) 1.11 m ) ) A tree casts a shadow of meters when the angle of elevation of the sun is 4. Find the height of the tree to the nearest meter. A) 1 m B) 1 m C) 10 m D) 11 m ) 9

10 4) A twenty-five foot ladder just reaches the top of a house and forms an angle of 41. with the wall of the house. How tall is the house? Round your answer to the nearest 0.1 foot. A) 19 ft B) 18. ft C) 18. ft D) 18.8 ft 4) A point on the terminal side of angle θ is given. Find the exact value of the indicated trigonometric function. ) (9, 1) Find sin θ. ) A) 4 B) 4 C) D) 4 ) (9, -8) Find tan θ. ) A) - B) C) D) 4 ) (-, -) Find sec θ. ) A) B) - 1 C) D) 1 8) - 1, Find cot θ. 8) A) - B) - C) D) - 9) (-, -1) Find cot θ. A) B) - 1 C) 1 D) 1 9) Use a coterminal angle to find the exact value of the expression. Do not use a calculator. 80) sin -1 A) - B) - 1 C) D) 1 80) 81) csc -0 81) A) B) 1 C) D) 8) cot 0 A) 1 B) 0 C) -1 D) undefined 8) 8) csc π 4 8) A) B) C) D) 84) tan (49π) A) 0 B) -1 C) 1 D) undefined 84) 10

11 Name the quadrant in which the angle θ lies. 8) cos θ < 0, csc θ < 0 A) I B) II C) III D) IV 8) 8) cot θ < 0, cos θ > 0 A) I B) II C) III D) IV 8) 8) tan θ < 0, sin θ < 0 A) I B) II C) III D) IV 8) 88) sin θ > 0, cos θ > 0 A) I B) II C) III D) IV 88) Find the reference angle of the given angle. 89) 8 A) 1 B) 18 C) 8 D) 10 89) 90) 4 A) 1 B) 114 C) 4 D) 90) 91) -0 A) 100 B) 10 C) 80 D) 10 91) 9) π 9) A) 4π B) π C) π D) π 9) - π 9) A) π B) π C) 4π D) π 94) - 4π 8 94) A) π 4 B) π C) π 8 D) π Use the reference angle to find the exact value of the expression. Do not use a calculator. 9) sin A) 1 B) C) - D) - 1 9) 9) csc -π 9) A) - B) - 1 C) - D) - 11

12 9) cot -11π 9) A) B) - C) D) - f(x) = sin x, g(x) = cos x, h(x) = tan x, F(x) = csc x, G(x) = sec x, H(x) = cot x. Provide an appropriate response. 98) Find f( ). What point is on the graph of f? A) - ;, - B) - ; -, 98) C) ;, D) ;, 99) Find g π. What point is on the graph of g? 99) A) ; π, B) 1 ; π, 1 C) - ; π, - D) - 1 ; π, - 1 Find the exact value of the indicated trigonometric function of θ. 100) cos θ =, tan θ < 0 Find sin θ. 100) A) - 1 B) - C) - 1 D) ) sec θ = 9, θ in quadrant IV Find tan θ. 101) A) - 9 B) - 9 C) - D) - 10) cos θ = 4, π < θ < π Find cot θ. A) - 4 B) -4 C) 4 D) ) 10) sin θ = 1, sec θ < 0 Find cos θ and tan θ. 10) A) cos θ =, tan θ = B) cos θ = -, tan θ = - C) cos θ =, tan θ = - D) cos θ = -, tan θ = 1

13 Solve the problem. 104) If sin θ = 1, find csc θ. 104) A) - 1 B) C) D) undefined The point P on the unit circle that corresponds to a real number t is given. Find the indicated trigonometric function. 10) 8, 8 A) Find sin t. B) 8 C) D) 8 10) 10) - 8, 8 Find cot t. 10) A) 8 B) - C) 8 D) ) - 4, - 4 Find cot t. 10) A) - B) C) - D) 4 108), - 10 Find csc t. 108) A) B) C) - 10 D) The point P on the circle x + y = r that is also on the terminal side of an angle θ in standard position is given. Find the indicated trigonometric function. 109) (-, 4) Find cos θ. 109) A) - 4 B) - C) 4 D) 110) (-, ) Find cot θ. A) - B) 1 C) - 1 D) - 110) 111) (-, -1) Find sec θ. A) - 10 B) - 10 C) D) ) 1

14 Solve the problem. 11) For what numbers θ is f(θ) = sec θ not defined? A) multiples of π (180 ) B) all real numbers 11) C) odd multiples of π (90 ) D) odd multiples of π (180 ) 11) What is the range of the cosine function? A) all real numbers greater than or equal to 1 or less than or equal to -1 B) all real numbers from -1 to 1, inclusive C) all real numbers D) all real numbers greater than or equal to 0 11) 114) What is the range of the secant function? A) all real numbers greater than or equal to 1 or less than or equal to -1 B) all real numbers from -1 to 1, inclusive 114) C) all real numbers, except odd multiples of π (90) D) all real numbers Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. 11) sin 40 11) A) 1 B) - C) - 1 D) 11) csc 0 A) - B) - 1 C) - D) - 11) 11) tan 900 A) B) 0 C) -1 D) undefined 11) 118) sin 1π 118) A) - B) - 1 C) -1 D) Find the exact value of the expression. Do not use a calculator. 119) cos (-π) + sin π 119) A) B) - C) -1 D) 0 10) csc π - sec -8π A) 1 B) -1 C) - D) 10) 14

15 Use the even-odd properties to find the exact value of the expression. Do not use a calculator. 11) cos (-0 ) A) - B) C) - 1 D) 1 11) 1) cos (-0 ) 1) A) 1 B) - C) D) - 1 1) sin (-10 ) 1) A) - B) 1 C) -1 D) 14) csc - π 14) A) - B) C) - D) 1) cos (-π) A) 0 B) 1 C) -1 D) undefined 1) 1

16 Answer Key Testname: REVIEW TEST 1 TRIG 1) C ) A ) C 4) C ) D ) D ) B 8) B 9) A 10) B 11) C 1) C 1) 9 mi 14) D 1) A 1) C 1) C 18) D 19) C 0) B 1) D ) B ) C 4) D ) C ) D ) D 8) D 9) D 0) A 1) A ) C ) B 4) A ) D ) B ) A 8) B 9) B 40) A 41) B 4) A 4) C 44) B 4) C 4) A 4) A 48) B 49) D 0) D 1

17 Answer Key Testname: REVIEW TEST 1 TRIG 1) A ) B ) D 4) B ) D ) D ) D 8) C 9) D 0) D 1) C ) D ) D 4) C ) A ) A ) B 8) D 9) B 0) B 1) B ) C ) B 4) C ) A ) B ) B 8) B 9) D 80) C 81) C 8) D 8) B 84) A 8) C 8) D 8) D 88) A 89) C 90) D 91) C 9) D 9) D 94) A 9) B 9) A 9) C 98) A 99) B 100) A 1

18 Answer Key Testname: REVIEW TEST 1 TRIG 101) C 10) D 10) B 104) B 10) B 10) B 10) B 108) B 109) B 110) D 111) B 11) C 11) B 114) A 11) D 11) C 11) B 118) A 119) B 10) A 11) D 1) C 1) A 14) C 1) C 18