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Trigonometry, 2nd Edition Test Bank

Trigonometry, 2nd Edition Test Bank makes exam preparation simple with structured and comprehensive questions.

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    Ch. 1 Angles and the Trigonometric Functions 1.1 Angles and Radian Measure 1 Recognize and Use the Vocabulary of Angles MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. The given angle is in standard position. Determine the quadrant in which the angle lies. 1) - 347° A) Quadrant I B) Quadrant II C) Quadrant III D) Quadrant IV 2) - 185° A) Quadrant II B) Quadrant I C) Quadrant III D) Quadrant IV 3) 203° A) Quadrant III B) Quadrant I C) Quadrant II D) Quadrant IV 4) - 12° A) Quadrant IV B) Quadrant I C) Quadrant II D) Quadrant III 2 Use Degree Measure MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Classify the angle as acute, right, obtuse, or straight. 1) 36° A) acute B) obtuse C) straight D) right 2) 134° A) obtuse B) right C) straight D) acute 3) 5.54° A) acute B) right C) obtuse D) straight 4) 107.621° A) obtuse B) acute C) right D) straight 5) π 2 A) right B) straight C) obtuse D) acute 6) π 6 A) acute B) right C) obtuse D) straight 7) 3 π 5 A) obtuse B) straight C) acute D) right Page 1

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    3 Use Radian Measure MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s. 1) r = 3 inches, s = 21 inches A) 7 radians B) 1 7 radians C) - 7 radians D) 7° 2) r = 1 3 feet, s = 7 feet A) 21 radians B) 7 3 radians C) 21° D) 7 3 ° 3) r = 1.5 meters, s = 2.25 meters A) 1.5 radians B) 0.67 radians C) 1.4 radians D) 0.75 radians 4) r = 1 meter, s = 400 centimeters A) 4 radians B) 1 400 radians C) 400 radians D) 40 radians 4 Convert Between Degrees and Radians MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Convert the angle in degrees to radians. Express answer as a multiple of π . 1) 36° A) π 5 radians B) π 6 radians C) π 7 radians D) π 4 radians 2) - 90° A) - π 2 radians B) - π 3 radians C) - π 4 radians D) - π 8 radians 3) 105° A) 7 π 12 radians B) 8 π 13 radians C) 6 π 11 radians D) 1 2 π radians 4) - 54° A) - 3 π 10 radians B) - 4 π 11 radians C) - 2 π 9 radians D) - 1 5 π radians Convert the angle in radians to degrees. 5) π 4 A) 45° B) 1° C) π 4 ° D) 45 π ° 6) - π 2 A) - 90° B) - 2° C) - π 2 ° D) - 90 π ° Page 2

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    7) 11 2 π A) 990° B) 1980° C) 164° D) 33 π ° 8) - 47 18 π A) - 470° B) - 940 π ° C) - 8° D) - 235° Convert the angle in degrees to radians. Round to two decimal places. 9) 254° A) 4.43 radians B) 4.42 radians C) 4.41 radians D) 4.4 radians 10) - 73° A) - 1.27 radians B) - 1.26 radians C) - 1.25 radians D) - 1.24 radians Convert the angle in radians to degrees. Round to two decimal places. 11) 4 3 π radians A) 240° B) 241° C) 242° D) 239° 12) 2 radians A) 114.59° B) 113.4° C) 0.03° D) - 0.13° 13) - 7.81 radians A) - 447.48° B) - 446.59° C) - 0.14° D) - 0.08° 5 Draw Angles in Standard Position MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Draw the angle in standard position. 1) 2 π 3 A) B) C) D) Page 3

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    2) 7 π 4 A) B) C) D) Page 4

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    3) 13 π 6 A) B) C) D) 4) - 3 π 4 A) B) C) D) Page 5

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    5) - 7 π 6 A) B) C) D) 6) 60° A) B) C) D) Page 6

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    7) - 150° A) B) C) D) 8) 330° A) B) C) D) Page 7

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    9) - 120° A) B) C) D) 10) 405° A) B) C) D) 6 Find Coterminal Angles MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find a positive angle less than 360° or 2 π that is coterminal with the given angle. 1) - 17° A) 343° B) 163° C) 523° D) 17° Page 8

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    2) 512° A) 152° B) 332° C) 256° D) 142° 3) - 1169° A) 271° B) 809° C) 89° D) 91° 4) 11 π 5 A) π 5 B) 6 π 5 C) - π 5 D) 4 π 5 5) 16 π 5 A) 6 π 5 B) - 16 π 5 C) 11 π 5 D) 4 π 5 6) - 13 π 9 A) 5 π 9 B) 23 π 9 C) 14 π 9 D) 13 π 9 7 Find the Length of a Circular Arc MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the length of the arc on a circle of radius r intercepted by a central angle θ . Round answer to two decimal places. 1) r = 4 centimeters, θ = 55° A) 3.84 centimeters B) 4.22 centimeters C) 3.46 centimeters D) 3.07 centimeters 2) r = 50 inches, θ = 45° A) 39.27 inches B) 41.7 inches C) 40.56 inches D) 37.42 inches 3) r = 12.40 inches, θ = 30° A) 6.49 inches B) 6.59 inches C) 6.69 inches D) 6.79 inches Solve the problem. 4) The minute hand of a clock is 7 inches long. How far does the tip of the minute hand move in 50 minutes? If necessary, round the answer to two decimal places. A) 36.65 inches B) 39.16 inches C) 37.88 inches D) 34.91 inches 5) A pendulum swings through an angle of 20° each second. If the pendulum is 35 inches long, how far does its tip move each second? If necessary, round the answer to two decimal places. A) 12.22 inches B) 14.65 inches C) 13.51 inches D) 10.37 inches 6) A car wheel has a 16 - inch radius. Through what angle (to the nearest tenth of a degree) does the wheel turn when the car rolls forward 5 ft? A) 214.9° B) 219.9° C) 224.9° D) 229.9° Page 9

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    7) A wheel with a 40 - inch radius is marked at two points on the rim. The distance between the marks along the wheel is found to be 12 inches. What is the angle (to the nearest tenth of a degree) between the radii to the two marks? A) 17.2° B) 19.2° C) 15.2° D) 13.2° 8 Find the Area of a Sector MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the area of the sector of a circle of radius r formed by a central angle θ . Express area in terms of π . Then round to two decimal places. 1) r = 6 m, θ = 120° A) 12 π ≈ 37.70 sq m B) 24 π ≈ 75.40 sq m C) 2 π ≈ 6.28 sq m D) 2160 π ≈ 6785.84 sq m Find the measure of the central angle on a circle of radius r that forms a sector with the given area, A. 2) r = 7 feet, A = 49 square feet A) 2 radians B) 14 radians C) 3 radians D) 1 radian Solve the problem. 3) A lawn sprinkler rotates through an angle of 105° and projects water over a distance of 60 feet. What is the area of the lawn watered by the sprinkler? Express the answer in terms of π and then round to two decimal places. A) 1050 π ≈ 3298.67sq ft B) 525 π ≈ 1649.34 sq ft C) 1470 π ≈ 4618.14 sq ft D) 2100 π ≈ 6597.34 sq ft 9 Use Linear and Angular Speed to Describe Motion on a Circular Path MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Express the angular speed in radians per second. 1) 420 revolutions per second A) 840 π radians per second B) 840 radians per second C) 420 π radians per second D) 420 radians per second Solve the problem. 2) A gear with a radius of 32 centimeters is turning at π 9 radians per sec. What is the linear speed at a point on the outer edge of the gear? A) 32 π 9 centimeters per second B) 9 π 32 centimeters per second C) 288 π centimeters per second D) π 288 centimeters per second 3) A car is traveling at 34 mph. If its tires have a diameter of 25 inches, how fast are the car's tires turning? Express the answer in revolutions per minute. If necessary, round to two decimal places. A) 457.14 revolutions per minute B) 2872.32 revolutions per minute C) 439.14 revolutions per minute D) 914.29 revolutions per minute Page 10

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    4) To approximate the speed of a river, a circular paddle wheel with radius 0.65 feet is lowered into the water. If the current causes the wheel to rotate at a speed of 12 revolutions per minute, what is the speed of the current? Express the answer in miles per hour rounded to two decimal places, if necessary. A) 0.56 miles per hour B) 0.09 miles per hour C) 49.01 miles per hour D) 0.28 miles per hour 5) A pick - up truck is fitted with new tires which have a diameter of 41 inches. How fast will the pick - up truck be moving when the wheels are rotating at 335 revolutions per minute? Express the answer in miles per hour rounded to the nearest whole number. A) 41 miles per hour B) 7 miles per hour C) 50 miles per hour D) 20 miles per hour 6) A carousel has a radius of 17 feet and takes 25 seconds to make one complete revolution. What is the linear speed of the carousel at its outside edge? Express the answer in feet per second. If necessary, round the answer to two decimal places. A) 4.27 feet per second B) 0.68 feet per second C) 9.24 feet per second D) 106.81 feet per second 1.2 Right Triangle Trigonometry 1 Use Right Triangles to Evaluate Trigonometric Functions MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the Pythagorean Theorem to find the length of the missing side.Then find the indicated trigonometric function of the given angle. Give an exact answer with a rational denominator. 1) Find sin θ . 8 5 A) 8 89 89 B) 5 89 89 C) 89 8 D) 89 5 2) Find csc θ . 9 10 A) 181 10 B) 181 9 C) 10 181 181 D) 9 181 181 Page 11

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    3) Find cos θ . 7 4 A) 4 65 65 B) 65 7 C) 65 4 D) 7 65 65 4) Find sec θ . 10 7 A) 149 10 B) 10 149 149 C) 10 149 7 D) 7 149 149 5) Find tan θ . 7 9 A) 7 9 B) 9 7 C) 130 9 D) 130 7 6) Find cot θ . 9 2 A) 2 9 B) 2 85 85 C) 9 2 D) 9 85 85 Page 12

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    7) Find sin θ . 10 9 A) 9 10 B) 10 19 19 C) 9 19 19 D) 19 10 2 Find Function Values for 30°( π /6), 45°( π /4), and 60°( π /3) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the given triangles to evaluate the expression. Rationalize all denominators. 1) csc 30° A) 2 B) 2 3 3 C) 1 2 D) 2 2) sec 60° A) 2 B) 2 3 3 C) 3 2 D) 2 3) cos 45° A) 2 2 B) 2 C) 3 2 D) 1 2 4) sin π 6 A) 1 2 B) 3 2 C) 3 3 D) 2 2 5) cot π 3 A) 3 3 B) 3 C) 1 2 D) 1 Page 13

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    6) cot π 4 A) 1 B) 2 3 3 C) 2 2 D) 2 7) tan 45° - sin 60° A) 2 - 3 2 B) 2 3 - 3 2 6 C) 2 - 2 2 D) - 3 6 8) cot 60° - cos 45° A) 2 3 - 3 2 6 B) 2 - 2 2 C) 2 - 3 2 D) 2 2 - 3 3 6 9) tan π 6 - sin π 3 A) - 3 6 B) 3 C) - 6 2 D) 2 3 - 3 2 6 3 Recognize and Use Fundamental Identities MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. θ is an acute angle and sin θ and cos θ are given. Use identities to find the indicated value. 1) sin θ = 5 7 , cos θ = 2 6 7 . Find csc θ . A) 7 5 B) 7 6 12 C) 2 6 5 D) 5 6 12 2) sin θ = 5 7 , cos θ = 2 6 7 . Find tan θ . A) 5 6 12 B) 7 6 12 C) 5 6 5 D) 7 5 3) sin θ = 7 4 , cos θ = 3 4 . Find sec θ . A) 4 3 B) 4 7 7 C) 3 7 7 D) 7 3 4) sin θ = - 5 3 , cos θ = 2 3 . Find cot θ . A) - 2 5 5 B) - 3 5 5 C) 3 2 D) 5 2 θ is an acute angle and sin θ is given. Use the Pythagorean identity sin 2 θ + cos 2 θ = 1 to find cos θ . 5) sin θ = 5 3 A) 2 3 B) 5 2 C) 3 2 D) 3 5 5 Page 14

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    Use an identity to find the value of the expression. Do not use a calculator. 6) sin 2 70° + cos 2 70° A) 1 B) 0 C) 0.70 D) 0.49 7) sec 2 55° - tan 2 55° A) 1 B) 0 C) 0.55 D) 0.30 8) sin 55° csc 55° A) 1 B) 0 C) 55 D) - 1 9) tan 20° - sin 20° cos 20° A) 0 B) 1 C) 20 D) Undefined 10) sin 14° csc 14° A) 1 B) 0 C) 14 D) sin 2 14° 11) cos 46° sec 46° A) 1 B) 0 C) 46 D) cos 2 46° 4 Use Equal Cofunctions of Complements MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find a cofunction with the same value as the given expression. 1) sin 67° A) cos 23° B) cos 67° C) tan 23° D) cot 23° 2) cos 14° A) sin 76° B) sin 14° C) sec 14° D) csc 76° 3) tan 75° A) cot 15° B) cot 75° C) sec 75° D) cot 165° 4) csc 5° A) sec 85° B) sec 5° C) sin 5° D) sec 95° 5) sin π 10 A) cos 2 π 5 B) sin 2 π 5 C) cos π 10 D) sin π 10 6) cos π 11 A) sin 9 π 22 B) cos 9 π 22 C) cos π 11 D) sin π 11 7) tan π 14 A) cot 3 π 7 B) tan 3 π 7 C) cot π 14 D) csc π 14 Page 15

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    8) csc π 13 A) sec 11 π 26 B) csc 11 π 26 C) cot π 13 D) csc π 13 5 Evaluate Trigonometric Functions with a Calculator MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use a calculator to find the approximate value of the expression. Round the answer to two decimal places. 1) sin 27° A) 0.45 B) 0.51 C) 0.96 D) 0.90 2) cos 17° A) 0.96 B) 1.04 C) - 0.28 D) - 0.20 3) cos 5° A) 1.00 B) - 0.28 C) - 1.00 D) 0.28 4) tan 72° A) 3.08 B) 3.01 C) - 0.26 D) - 0.33 5) csc 40° A) 1.56 B) 1.46 C) 1.34 D) 1.24 6) cot 0.2038 A) 4.84 B) 0.21 C) 0.98 D) 1.02 7) cot π 7 A) 2.08 B) 2.21 C) 127.66 D) 127.53 8) cos 3 π 5 A) - 0.31 B) - 0.20 C) 1.00 D) 1.11 9) sec π 5 A) 1.24 B) 1.10 C) 1.00 D) 0.86 Find the measure of the side of the right triangle whose length is designated by a lowercase letter. Round your answer to the nearest whole number. 10) a 36° b = 11 A) a = 8 cm B) a = 15 cm C) a = 6 cm D) a = 1 cm Page 16

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    Use a calculator to find the value of the acute angle θ to the nearest degree. 11) tan θ = 13.2894 A) 86° B) 1° C) 88° D) 24° Use a calculator to find the value of the acute angle θ in radians, rounded to three decimal places. 12) sin θ = 0.8659 A) 1.047 radians B) 59.986 radians C) 5.999 radians D) 0.524 radians 6 Use Right Triangle Trigonometry to Solve Applied Problems MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) A surveyor is measuring the distance across a small lake. He has set up his transit on one side of the lake 80 feet from a piling that is directly across from a pier on the other side of the lake. From his transit, the angle between the piling and the pier is 30°. What is the distance between the piling and the pier to the nearest foot? A) 46 feet B) 40 feet C) 69 feet D) 139 feet 2) A building 150 feet tall casts a 70 foot long shadow. If a person stands at the end of the shadow and looks up to the top of the building, what is the angle of the person's eyes to the top of the building (to the nearest hundredth of a degree)? (Assume the person's eyes are 5 feet above ground level.) A) 64.23° B) 64.98° C) 61.13° D) 28.87° 3) A radio transmission tower is 120 feet tall. How long should a guy wire be if it is to be attached 11 feet from the top and is to make an angle of 26° with the ground? Give your answer to the nearest tenth of a foot. A) 248.6 feet B) 273.7 feet C) 121.3 feet D) 133.5 feet 4) A straight trail with a uniform inclination of 16° leads from a lodge at an elevation of 500 feet to a mountain lake at an elevation of 9700 feet. What is the length of the trail (to the nearest foot)? A) 33,377 feet B) 35,191 feet C) 9571 feet D) 10,091 feet 5) A building 180 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 person's eyes are level with the top of the building.) A) 24° B) 66° C) 64° D) 26° 7 Additional Concepts MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the exact value of the expression. Do not use a calculator. 1) 1 + sin 2 45° + sin 2 45° A) 2 B) 0 C) - 1 D) 1 2) 1 - tan 2 75° + csc 2 15° A) 2 B) 0 C) - 1 D) 1 3) cos 5°sin 85° + sin 5°cos 85° A) 1 B) 0 C) - 1 D) 2 Page 17

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    4) If tan θ = 11, find the exact value of cot π 2 - θ . A) 11 B) 1 11 C) 10 D) 12 1.3 Trigonometric Functions of Any Angle 1 Use the Definitions of Trigonometric Functions of Any Angle MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. A point on the terminal side of angle θ is given. Find the exact value of the indicated trigonometric function of θ . 1) (6, 8) Find sin θ . A) 4 5 B) 3 5 C) 3 4 D) 4 3 2) (21, 28) Find cos θ . A) 3 5 B) 4 5 C) 3 4 D) 4 3 3) ( - 20, 48) Find sin θ . A) 12 13 B) 5 13 C) - 5 13 D) - 12 13 4) (3, 4) Find csc θ . A) 5 4 B) 5 3 C) 3 4 D) 4 3 5) (6, 8) Find tan θ . A) 4 3 B) 3 4 C) 3 5 D) 4 5 6) (3, - 4) Find sin θ . A) - 4 5 B) 3 5 C) 5 3 D) - 4 7) ( - 3, - 4) Find sec θ . A) - 5 3 B) 5 4 C) 4 3 D) - 3 5 8) ( - 1 3 , 1 2 ) Find cos θ . A) - 2 13 13 B) 3 13 13 C) - 13 3 D) 13 2 9) ( - 9, - 4) Find cot θ . A) 9 4 B) 4 9 C) - 9 10 D) - 2 5 Page 18

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    Evaluate the trigonometric function at the quadrantal angle, or state that the expression is undefined. 10) csc π A) undefined B) 0 C) - 1 D) 1 11) tan π 2 A) undefined B) - 1 C) 1 D) 0 2 Use the Signs of the Trigonometric Functions MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Let θ be an angle in standard position. Name the quadrant in which the angle θ lies. 1) tan θ < 0, sin θ < 0 A) quadrant IV B) quadrant I C) quadrant II D) quadrant III Find the exact value of the indicated trigonometric function of θ . 2) cos θ = 4 9 , tan θ < 0 Find sin θ . A) - 65 9 B) - 65 4 C) - 9 4 D) - 65 3) sec θ = 9 4 , θ in quadrant IV Find tan θ . A) - 65 4 B) - 65 9 C) - 9 4 D) - 65 4) sin θ = - 8 9 , tan θ > 0 Find sec θ . A) - 9 17 17 B) - 17 9 C) 9 8 D) - 8 17 17 5) csc θ = - 9 2 , θ in quadrant III Find cot θ . A) 77 2 B) - 9 77 77 C) - 77 9 D) - 2 77 77 6) tan θ = - 2 5 , θ in quadrant II Find cos θ . A) - 5 29 29 B) 5 29 29 C) 29 2 D) - 29 5 7) cot θ = - 7 4 , cos θ < 0 Find csc θ . A) 65 4 B) - 7 65 65 C) 7 65 65 D) - 65 7 Page 19

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    8) tan θ = - 15 8 , 90° < θ < 180° Find cos θ . A) - 8 17 B) - 8 C) - 8 23 23 D) - 15 23 23 9) cos θ = 20 29 , 3 π 2 < θ < 2 π Find cot θ . A) - 20 21 B) - 20 3 C) - 21 20 D) 29 20 3 Find Reference Angles MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the reference angle for the given angle. 1) 42° A) 42° B) 48° C) 138° D) 132° 2) 129° A) 51° B) 39° C) 61° D) 49° 3) 395° A) 35° B) 55° C) 145° D) 125° 4) - 383° A) 23° B) 67° C) 157° D) 113° 5) - 12° A) 12° B) 78° C) 168° D) 102° 6) - 240° A) 60° B) 30° C) 150° D) 120° 7) - 79.7° A) 79.7° B) 10.3° C) 80.2° D) 10.8° 8) 13 π 12 A) π 12 B) 11 π 12 C) π 24 D) 13 π 12 9) 3 π 4 A) π 4 B) 3 π 4 C) 5 π 4 D) π 8 10) - 9 π 8 A) π 8 B) 7 π 8 C) 9 π 8 D) π 16 Page 20

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    11) - 3 π 4 A) π 4 B) 3 π 4 C) 5 π 4 D) π 8 12) 5.2 A) 1.08 B) - 2.06 C) 2.06 D) - 1.08 13) 23 π 3 A) π 3 B) 2 π 3 C) - π 3 D) 16 π 3 14) - 13 π 3 A) π 3 B) 2 π 3 C) - π 3 D) 7 π 3 4 Use Reference Angles to Evaluate Trigonometric Functions MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use reference angles to find the exact value of the expression. Do not use a calculator. 1) sin 4 π 3 A) - 3 2 B) 3 2 C) - 1 D) - 1 2 2) tan 7 π 6 A) 3 3 B) 3 C) - 3 D) 3 2 3) tan - 7 π 4 A) 1 B) 3 C) 3 3 D) - 1 4) csc 5 π 3 A) - 2 3 3 B) - 2 C) - 3 D) - 1 2 5) sec - 3 π 4 A) - 2 B) - 2 3 3 C) - 2 D) 2 2 Page 21

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    6) cot - 5 π 6 A) 3 B) - 3 C) 3 3 D) - 3 3 7) cos 3 π 2 A) 0 B) 1 C) - 1 D) undefined 8) tan - π 2 A) - 1 B) 1 C) 0 D) undefined 9) sin 495° A) 2 2 B) 1 2 C) - 1 2 D) - 2 2 10) tan 750° A) 3 3 B) 3 C) - 3 D) 3 2 11) csc 1020° A) - 2 3 3 B) - 2 C) - 3 D) - 1 2 12) cot 570° A) 3 B) - 3 C) 3 3 D) - 3 3 13) tan 34 π 3 A) 3 B) - 3 C) 3 3 D) - 3 3 14) cot - 8 π 3 A) 3 3 B) - 3 C) 3 D) - 3 3 Page 22

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    1.4 Trigonometric Functions: The Unit Circle 1 Use a Unit Circle to Define Trigonometric Functions of Real Numbers MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. The point P(x, y) on the unit circle that corresponds to a real number t is given. Find the values of the indicated trigonometric function at t. 1) 3 4 , 7 4 Find sin t. A) 7 4 B) 3 4 C) 7 3 D) 3 7 7 2) 5 6 , 11 6 Find tan t. A) 11 5 B) 6 5 C) 11 6 D) 5 11 11 3) 39 8 , 5 8 Find sec t. A) 8 39 39 B) 8 5 C) 39 5 D) 5 39 39 4) - 39 8 , 5 8 Find cos t. A) - 39 8 B) 5 8 C) - 39 5 D) - 8 39 39 5) - 21 5 , 2 5 Find cot t. A) - 21 2 B) 2 5 C) 21 5 D) - 5 2 6) - 21 5 , - 2 5 Find sin t. A) - 2 5 B) - 21 5 C) - 5 21 21 D) 5 2 7) - 65 9 , - 4 9 Find cot t. A) 65 4 B) - 65 4 C) - 4 65 65 D) 65 9 8) 3 8 , - 55 8 Find csc t. A) - 8 55 55 B) - 55 8 C) 55 3 D) 55 8 Page 23

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    9) 3 4 , - 7 4 Find cos t. A) 3 4 B) - 7 4 C) 7 4 D) - 3 4 10) 5 7 , - 2 6 7 Find csc t. A) - 7 6 12 B) 7 5 C) - 6 10 D) 5 7 Use the unit circle to find the value of the trigonometric function. 11) tan π 6 A) 3 3 B) 3 C) 3 2 D) 1 12) tan π 3 A) 3 B) 3 3 C) 3 2 D) 2 13) csc 5 π 3 A) - 2 3 3 B) - 3 2 C) 2 D) - 1 2 14) cot 3 π 2 A) 0 B) 1 C) - 1 D) undefined 2 Recognize the Domain and Range of Sine and Cosine Functions MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) What is the domain of the sine function? A) all real numbers B) all real numbers from - 1 to 1, inclusive C) all real numbers, except odd multiples of π 2 (90°) D) all real numbers, except integral multiples of π (180°) 2) What is the range of the cosine function? A) all real numbers from - 1 to 1, inclusive B) all real numbers C) all real numbers greater than or equal to 1 or less than or equal to - 1 D) all real numbers greater than or equal to 0 Page 24

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    3 Use Even and Odd Trigonometric Functions MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use even and odd properties of the trigonometric functions to find the exact value of the expression. 1) sin - π 6 A) - 1 2 B) 1 2 C) 3 2 D) - 3 2 2) sin - π 3 A) - 3 2 B) 1 2 C) - 1 2 D) 3 2 3) cot - π 3 A) - 3 3 B) 3 3 C) 3 D) - 3 4) sin - π 4 A) - 2 2 B) 2 2 C) 3 2 D) - 3 2 5) cot - π 6 A) - 3 B) 3 3 C) 3 D) - 3 3 6) csc - π 2 A) - 1 B) 1 C) 0 D) undefined 7) sec ( - π ) A) - 1 B) 1 C) 0 D) undefined 8) sin ( - 120°) A) - 3 2 B) - 1 2 C) 1 2 D) 3 2 Page 25

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    9) csc - π 6 A) - 2 B) 2 C) - 2 3 3 D) 2 3 3 10) sec - π 6 A) 2 3 3 B) 2 C) - 2 D) - 2 3 3 4 Use Periodic Properties MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use periodic properties of the trigonometric functions to find the exact value of the expression. 1) cos 10 π 3 A) - 1 2 B) - 3 2 C) 3 2 D) 1 2 2) sin 22 π 3 A) - 3 2 B) 3 2 C) - 1 D) - 1 2 3) cot 21 π 4 A) 1 B) 3 C) 3 3 D) - 1 4) tan 13 π A) 0 B) 1 C) undefined D) - 1 5) cos 11 π 2 A) 0 B) 1 C) - 1 D) undefined 5 Solve Apps: Trigonometric Functions MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) The mean air temperature T, in F°, at Fairbanks, Alaska, on the nth day of the year, 1 ≤ n ≤ 365, is approximated by: T = 37 sin( 2 π 365 (n - 101)) + 25. Find the temperature at Fairbanks on day 176, to the nearest tenth. A) 60.6° F B) 90.9° F C) 57.6° F D) 56.1° F Page 26

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    2) The total sales in dollars of some small businesses fluctuates according to the equation S = A + B sin π 6 x, where x is the time in months, with x = 1 corresponding to January, A = 6700, and B = 4000. Determine the month with the greatest total sales and give the sales in that month. A) March; $10,700 B) June; $6700 C) September; $2700 D) December; $10,700 3) The height of the water, H, in feet, at a boat dock t hours after 7 A.M is given by E = 12 + 1.5 cos π 60 t, where t is time measured in seconds. Find the period. A) 120 B) π 120 C) 1 120 D) 120 π Page 27

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    Ch. 1 Angles and the Trigonometric Functions Answer Key 1.1 Angles and Radian Measure 1 Recognize and Use the Vocabulary of Angles 1) A 2) A 3) A 4) A 2 Use Degree Measure 1) A 2) A 3) A 4) A 5) A 6) A 7) A 3 Use Radian Measure 1) A 2) A 3) A 4) A 4 Convert Between Degrees and Radians 1) A 2) A 3) A 4) A 5) A 6) A 7) A 8) A 9) A 10) A 11) A 12) A 13) A 5 Draw Angles in Standard Position 1) A 2) A 3) A 4) A 5) A 6) A 7) A 8) A 9) A 10) A 6 Find Coterminal Angles 1) A 2) A 3) A 4) A 5) A Page 28

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    6) A 7 Find the Length of a Circular Arc 1) A 2) A 3) A 4) A 5) A 6) A 7) A 8 Find the Area of a Sector 1) A 2) A 3) A 9 Use Linear and Angular Speed to Describe Motion on a Circular Path 1) A 2) A 3) A 4) A 5) A 6) A 1.2 Right Triangle Trigonometry 1 Use Right Triangles to Evaluate Trigonometric Functions 1) A 2) A 3) A 4) A 5) A 6) A 7) A 2 Find Function Values for 30°( π /6), 45°( π /4), and 60°( π /3) 1) A 2) A 3) A 4) A 5) A 6) A 7) A 8) A 9) A 3 Recognize and Use Fundamental Identities 1) A 2) A 3) A 4) A 5) A 6) A 7) A 8) A 9) A 10) A 11) A Page 29

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    4 Use Equal Cofunctions of Complements 1) A 2) A 3) A 4) A 5) A 6) A 7) A 8) A 5 Evaluate Trigonometric Functions with a Calculator 1) A 2) A 3) A 4) A 5) A 6) A 7) A 8) A 9) A 10) A 11) A 12) A 6 Use Right Triangle Trigonometry to Solve Applied Problems 1) A 2) A 3) A 4) A 5) A 7 Additional Concepts 1) A 2) A 3) A 4) A 1.3 Trigonometric Functions of Any Angle 1 Use the Definitions of Trigonometric Functions of Any Angle 1) A 2) A 3) A 4) A 5) A 6) A 7) A 8) A 9) A 10) A 11) A 2 Use the Signs of the Trigonometric Functions 1) A 2) A 3) A 4) A 5) A Page 30

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