MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. A) 110 B) 120 C) 60 D) 150

Transcription

1 Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Convert the angle to decimal degrees and round to the nearest hundredth of a degree. ) 56 5 A) B) 56.6 C) D) ) Convert the angle to degrees, minutes, and seconds. ) 0.78 A) B) C) D) ) Find the angle of least positive measure coterminal with the given angle. ) 500 A) 50 B) 0 C) 0 D) 0 ) ) Find the measure of the smaller angle formed by the hands of the clock shown. ) A) 0 B) 0 C) 60 D) 50

2 Sketch an angle θ in standard position such that θ has the least positive measure and the given point is on the terminal side of θ. 5) (-, 5) 5) y x A) B) C) D) Use the appropriate identity to find the indicated function value. Rationalize the denominator, if applicable. If the given value is a decimal, round your answer to three decimal places. 6) tan θ, given that cot θ = ) A) 7 B) 7 6 C) D) Identify the quadrant for the angle θ satisfying the following conditions. 7) cot θ < 0 and cos θ > 0 A) Quadrant II B) Quadrant IV C) Quadrant I D) Quadrant III 7)

3 Evaluate the function requested. Write your answer as a fraction in lowest terms. 8) 8) 8 0 Find sin A. A) sin A = B) sin A = 5 C) sin A = 5 D) sin A = 5 Without using a calculator, give the exact trigonometric function value with rational denominator. 9) cos 60 A) B) C) D) 9) Solve the problem for the given information. 0) Find the equation of a line passing through the origin so that the cosine of the angle between the line in quadrant I and the positive x-axis is. 0) A) y = x B) y = x C) y = x D) y = x Find a value of θ in [0, 90 ] that satisfies the statement. Leave answer in decimal degrees rounded to seven decimal places, if necessary. ) tan θ =.9579 ) A) B).888 C) D) Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. ) tan 6 8 ) A) B) C) D)

4 Solve the right triangle. If two sides are given, give angles in degrees and minutes. ) ) B = 68 ', b = 7 km Round side lengths to one decimal place. A) A = 6'; c = 8. km; a = 5.7 km B) A = 6'; c = 5.8 km; a = 8. km C) A = 6'; c = 5.8 km; a = 6.8 km D) A = 6'; c = 8. km; a = 6.8 km Find the corresponding angle measure in radians. ) 0 ) - r - A) π 6 B) π C) 7π 6 D) π Find the length of an arc intercepted by a central angle θ in a circle of radius r. Round your answer to decimal place. 5) r = 6. cm.; θ = 7 6 π radians 5) A) 7.9 cm B) 9.5 cm C) 0.5 cm D) 95.8 cm Find the exact value without using a calculator. 6) cos π 6) A) B) undefined C) - D) - Convert the radian measure to degrees. Round to the nearest hundredth if necessary. 7) 5π A) B) 75 C) 50 D) π 7)

5 Assume that the cities lie on the same north-south line and that the radius of the earth is 600 km. 8) Find the distance between City A, 6 N and City B, 9 N. (Round to the nearest kilometer.) A) 6 km B) 75 km C) 686 km D) 777 km 8) 9) Through how many radians will the hour hand on a clock rotate in 8 hours? A) 8π B) 6π C) π D) π 9) Convert the degree measure to radians. Leave answer as a multiple of π. 0) 50 A) 7π 8 B) 5π 8 C) 5π 6 D) 5π 9 0) ) The angle of elevation from a point on the ground to the top of a tower is 5 6. The angle of elevation from a point 0 feet farther back from the tower is 8. Find the height of the tower. Round to the nearest foot. A) 6 ft B) 6 ft C) 58 ft D) 7 ft ) ) On a sunny day, a tree and its shadow form the sides of a right triangle. If the hypotenuse is 0 meters long and the tree is meters tall, how long is the shadow? A) 5 m B) 7 m C) 6 m D) m ) Find all values of θ, if θ is in the interval [0, 60 ) and has the given function value. ) cos θ = - A) 60 and 0 B) 50 and 0 C) 0 and 0 D) 60 and 00 ) Solve the right triangle. ) B =., c =.6 mm, C = 90 Round values to one decimal place. A) a = mm, A = 55.6, b =.5 mm B) a =.8 mm, A = 55.6, b =.6 mm C) a =.6 mm, A = 55.6, b =.8 mm D) a =.8 mm, A = 55.6, b = mm ) Find the area of a sector of a circle having radius r and central angle θ. If necessary, express the answer to the nearest tenth. 5) r = 8.0 ft, θ = π radians 5) A) ft B) 9. ft C) 9.5 ft D) 8.8 ft 6) The grade resistance F of a car traveling up or down a hill is modeled by the equation F = W sin θ, where W is the weight of the car and θ is the angle of the hill's grade (θ > 0 for uphill travel, θ < 0 for downhill travel). What is the grade resistance (to the nearest pound) of a 000-lb car traveling uphill on a grade (θ = )? A) 00 lb B) -70 lb C) 70 lb D) -00 lb 6) 5

6 Find the exact circular function value. 7) sin π 7) A) - B) C) - D) Graph the function. 8) y = cos x 8) y -π π x - - A) y B) y -π π x -π π x C) y D) y -π π x -π π x

7 Use Identities to find the exact value. 9) cos 55 A) - 6 B) - 6 C) 6 - D) 6-9) Use a sum or difference identity to find the exact value. 0) sin 5 0) A) 6 + B) 6 - C) D) ) The voltage E in an electrical circuit is given by E =. cos 0πt, where t is time measured in seconds. Find the period. A) 70 B) 70π C) π D) ) The figure shows an angle θ in standard position with its terminal side intersecting the unit circle. Evaluate the indicated circular function value of θ. ) Find cos θ. ) - 5, A) - B) C) - 5 D) - 5 Find the exact value of the real number y. ) y = cos - ) A) π B) π 6 C) π 6 D) 7π 7

8 Use an identity to write the expression as a single trigonometric function or as a single number. ) + cos A) tan B) sin C) cot D) cos ) Find the exact value by using a half-angle identity. 5) sin 75 5) A) - - B) - C) + D) - + Use identities to find the indicated value for each angle measure. 6) sin θ = - 5, π < θ < π Find cos(θ). A) B) 7 5 C) - 5 D) 5 6) Use a sum or difference identity to find the exact value. 7) tan 75 A) - - B) - C) - + D) + 7) 8) Find ω for a spoke on a bike tire revolving 85 times per minute. A) π 70 radians per min B) 85π radians per min C) 70π radians per min D) π 85 radians per min 8) Find the exact values of s in the given interval that satisfy the given condition. 9) [0, π); cos s = 9) A) π, 5π B) π, 7π C) π, π D) π 6, π 6 Find the value of s in the interval [0, π/] that makes the statement true. Round to four decimal places. 0) cos s = A) B) 5.0 C) D) ) ) Find the radius of a circle in which a central angle of π 7 radian determines a sector of area ) 7 square meters. Round to the nearest hundredth. A) 7.9 m B) 5. m C) 0.86 m D).67 m 8

9 ) A pendulum swinging through a central angle of completes an arc of length. cm. What is the length of the pendulum? Round to the nearest hundredth. A).77 cm B).97 cm C).67 cm D).87 cm ) Find the exact value of the expression. ) sec 5 ) A) B) C) D) Find the reference angle for the given angle. ) -6. A) 6. B) 6. C) 6.6 D) 6.9 ) Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle. Rationalize the denominator if applicable. 5) Find sin A when a = 7 and b = 6. 5) A) B) 85 6 C) 85 7 D) Use the fundamental identities to find the value of the trigonometric function. 6) Find tan θ, given that sin θ = and θ is in quadrant II. 6) A) 5 B) C) - D) Determine the signs of the given trigonometric functions of an angle in standard position with the given measure. 7) csc (608 ) and cot (608 ) 7) A) negative and negative B) negative and positive C) positive and positive D) positive and negative If r is a positive number and the point (x, y) is in the indicated quadrant, decide whether the given ratio is positive or negative. 8) IV, x y 8) A) Positive B) Negative Evaluate the expression. 9) cos 50 9) A) B) Undefined C) D) 0 9

10 Suppose that θ is in standard position and the given point is on the terminal side of θ. Give the exact value of the indicated trig function for θ. 50) (6, 8); Find cos θ. 50) A) B) 5 C) D) 5 0

11 Answer Key Testname: FINAL REVIEWNET ) C ) D ) C ) B 5) B 6) C 7) B 8) B 9) A 0) C ) D ) B ) D ) D 5) D 6) C 7) B 8) C 9) A 0) B ) A ) D ) B ) B 5) B 6) C 7) D 8) C 9) A 0) B ) D ) C ) A ) D 5) C 6) A 7) D 8) C 9) A 0) C ) A ) D ) A ) A 5) D 6) B 7) B 8) B 9) D

12 Answer Key Testname: FINAL REVIEWNET 50) B