Group/In-Class Exercises 8/18/09 g0401larson8etrig.tst 4.1 Radian and Degree Measure

Transcription

1 Group/In-Class Exercises 8/8/09 g040larson8etrig.tst 4. Radian and Degree Measure Name 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. ) -57 A) Quadrant II B) Quadrant I C) Quadrant IV D) Quadrant III Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s. ) r = meter, s = 700 centimeters A) 700 radians B) 70 radians C) radians D) 7 radians 700 Convert the angle in degrees to radians. Express answer as a multiple of π. ) - 60 A) - 7 9π π radians B) radians C) - 7π 8 radians D) - 8π 9 radians Convert the angle in radians to degrees. Round to two decimal places. 4) 4π 7 radians A) 0.86 B) C) 0.86 D) 0.86 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find a positive angle less than 60 that is coterminal with the given angle. 7) - 4π 9 A) π 9 C) π 9 B) 4π 9 D) 4π 9 Solve the problem. 8) A car wheel has a 4-inch radius. Through what angle (to the nearest tenth of a degree) does the wheel turn when the car rolls forward ft? A) 54. B) 59. C) 49. D) 64. 9) A carousel has a radius of 0 feet and takes 5 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).59 feet per second B) feet per second C) 5.66 feet per second D) 0.57 feet per second SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Draw the angle in standard position. 5) 0 6) - 7π 6 ddda00dca

2 Answer Key Testname: G040LARSON8ETRIG )D )D )D 4)A 5) 6) 7)D 8)C 9)A

3 Solutions: Group/In-Class Exercises 4. Angles and Radian Measure - Trig: PBCC For text: Precalculus Larson 8e E:\My Documents All\My Documents USB\Math\xGroup\group_trig_f0_PC_Larson8\g040Larson8eTrig_sol.doc 4.

4 Group/In-Class Exercises 8/8/09 g040larson8etrig.tst 4. Trigonometric Functions: The Unit Circle Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. The point P on the unit circle that corresponds to a real number t is given. Find the values of the indicated trigonometric function at t. ) 5 7,- 6 7 A) 7 5 Find csc t. B) 5 7 Use even and odd properties of the trigonometric functions to find the exact value of the expression. 5) sec - π 6 A) - B) - C) D) C) D) Use an identity to find the value of the expression. Do not use a calculator. Use the unit circle to find the value of the trigonometric function. ) sin π A) 0 B) - C) D) undefined Find the exact value of the expression if θ = 45. Do not use a calculator. ) sin θ 6 A) C) 6 B) 6 D) Solve the problem. 4) The force acting on a pendulum to bring it to its perpendicular resting point is called the restoring force. The restoring force F, in Newtons, acting on a string pendulum is given by the formula F = mg sinθ where m is the mass in kilograms of the pendulum's bob, g 9.8 meters per second per second is the acceleration due to gravity, and θ is angle at which the pendulum is displaced from the perpendicular. What is the value of the restoring force when m = 0.5 kilogram and θ = 45? If necessary, round the answer to the nearest tenth of a Newton. A).4 N B). N C) 4. N D).5 N 6) csc π 4 - cot π 4 A) - B) π 4 C) D) - π 4 Use periodic properties of the trigonometric functions to find the exact value of the expression. 7) tan 5π 6 A) - B) C) - D) Use a calculator to find the value of the trigonometric function to four decimal places. 8) cot A).098 B) C).506 D) Solve the problem. 9) The height of the water, H, in feet, at a boat dock t hours after 7 A.M is given by E = cos π t, where t is time measured in 5 seconds. Find the period. A) π 50 B) 50 C) 50 D) 50π

5 Answer Key Testname: G040LARSON8ETRIG )C )B )A 4)D 5)C 6)C 7)C 8)C 9)C

6 Solutions: Group/In-Class Exercises 4. Trig Functions: Unit Circle - Trig: PBCC For text: Precalculus Larson 8e E:\My Documents All\My Documents USB\Math\xGroup\group_trig_f0_PC_Larson8\g040Larson8eTrig_sol.doc 4.

7 Group/In-Class Exercises 8/0/0 040Larson8eTrig.tst 4. Right Angle Trig Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given angle. Give an exact answer with a rational denominator. ) Find sin. A) sin = 5 9 C) sin = B) sin = 9 5 D) sin = 9 9 Solve. ) Given that sin = 5 and that the terminal side is in quadrant II, find tan. A) 4 B) - 4 C) 4 D) - 4 ) Given that sin = 5 and that the terminal side is in quadrant II, find cot. A) - 4 C) - 4 B) D) Solve the problem. 4) A radio transmission tower is 50 feet tall. How long should a guy wire be if it is to be attached 0 feet from the top and is to make an angle of with the ground? Give your answer to the nearest tenth of a foot. A) feet B) 69.6 feet C) 58.8 feet D) feet dbad

8 Group/In-Class Exercises 8/0/0 040Larson8eTrig.doc - Solutions 4. Right Angle Trig

9 Group/In-Class Exercises Name 8/0/0 0404Larson8eTrig.tst 4.4 Trig Functions of Any Value Larson8e MULTIPLE CHOICE. Choose the one alternative that best 7) cot -7 completes the statement or answers the question. 6 A point on the terminal side of angle is given. Find the exact value of the indicated trigonometric function of. ) (4, 9) Find tan. 9 A) B) A) - C) D) ccdbccc B) - C) 9 4 D) 5 Let be an angle in standard position. Name the quadrant in which the angle lies. ) sec < 0, tan < 0 A) quadrant IV B) quadrant I C) quadrant II D) quadrant III Find the exact value of the indicated trigonometric function of. ) tan = 0, 80 < < 70 Find cos. A) - B) C) D) - 9 Find the reference angle for the given angle. 4) -46 A) 4 B) 66 C) 4 D) 56 5) 9 8 A) 9 8 B) 7 8 C) 8 D) 6 Use reference angles to find the exact value of the expression. Do not use a calculator. 6) csc - A) - C) - B) - D) -

10 Group/In-Class Exercises 8/0/0 0404Larson8eTrig.tst - Solutions 4.4 Trig Functions of Any Value