Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 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. 1) csc, given that sin = -0.471 1) A) -.41 B).41 C) 1.171 D) -1.171 The triangles are similar. Find the missing side, angle or value of the variable. ) ) a = 6 b = 8 c = 5 d = e = 4 A) x = 5 B) x = 11 C) x = 10 D) x = 15 Use the fundamental identities to find the value of the trigonometric function. ) Find cos, given that tan = - 7 and is in quadrant II. ) A) 7 5 5 B) - 7 5 5 C) - 5 7 D) 5 Convert the angle to degrees, minutes, and seconds. 4) 140.54 4) A) 140 0 54 B) 140 54 C) 140 4 D) 140 4 Determine the signs of the given trigonometric functions of an angle in standard position with the given measure. 5) csc (608 ) and cot (608 ) 5) A) positive and positive B) negative and negative C) negative 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. 6) III, x y 6) A) Positive B) Negative Identify the quadrant for the angle satisfying the following conditions. 7) sin > 0 and cos < 0 7) A) Quadrant II B) Quadrant III C) Quadrant IV D) Quadrant I 1
Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, coterminal with the given angle. 8) 50 8) A) 0 and -10 B) 0 and -10 C) 410 and -10 D) 410 and -10 Sketch an angle in standard position such that has the least positive measure and the given point is on the terminal side of. 9) (, 6) 9) A) B) C) D)
The triangles are similar. Find the missing side, angle or value of the variable. 10) x and y 10) A) x = 17; y = 17 4 B) x = 1; y = C) x = 8; y = D) x = 10; y = 5 If n is an integer, n 180 represents an integer multiple of 180, and (n + 1) 90 represents an odd integer multiple of 90. Decide whether the expression is equal to 0, 1, -1, or is undefined. 11) tan(n 180 ) 11) A) -1 B) Undefined C) 1 D) 0 Provide an appropriate response. 1) Find the complement of an angle whose measure is 7. 1) A) 107 B) 7 C) 17 D) 16 Convert the angle to degrees, minutes, and seconds. 1) 40.78 1) A) 40 46 6 B) 40 46 78 C) 40 46 48 D) 40 46 54 Use the fundamental identities to find the value of the trigonometric function. 14) Find cos, given that tan = - 5 and sin > 0. 14) A) 5 9 9 B) - 9 5 C) 9 D) - 5 9 9 Decide whether the statement is possible or impossible for an angle. 15) sin = 5.46 15) A) Possible B) Impossible
Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, coterminal with the given angle. 16) -85 16) A) 175 and -5 B) 75 and -445 C) 85 and -105 D) 185 and -55 Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene. 17) 17) A) Acute, scalene B) Obtuse, scalene C) Acute, isosceles D) Obtuse, equilateral Determine the signs of the given trigonometric functions of an angle in standard position with the given measure. 18) cos (459 ) and tan (459 ) 18) A) positive and negative B) negative and negative C) negative and positive D) positive and positive 4
Sketch an angle in standard position such that has the least positive measure and the given point is on the terminal side of. 19) (-5, ) 19) A) B) C) D) Use the fundamental identities to find the value of the trigonometric function. 0) Find csc, given that cot = - 15 and is in quadrant II. 0) A) 1 4 B) 4 C) - 1 4 D) -4 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. 1) tan, given that cot = - 6 7 1) A) - 7 6 B) - 6 7 C) 7 6 D) 1 7 5
Convert the angle to decimal degrees and round to the nearest hundredth of a degree. ) 11 57 ) A) 1.0 B) 11.9 C) 11.97 D) 11.96 Identify the quadrant for the angle satisfying the following conditions. ) cos < 0 and csc < 0 ) A) Quadrant I B) Quadrant II C) Quadrant IV D) Quadrant III 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. 4) cot, given that tan = 0.407 4) A) 4.148 B) 4.155 C) 4.169 D) 4.16 Use the fundamental identities to find the value of the trigonometric function. 5) Find sin, given that cos = 4 7 and tan < 0. 5) A) - 7 B) - C) - 4 D) - 7 4 Perform the calculation. 6) 90-54 5 6) A) 5 5 B) 6 8 C) 5 8 D) 6 5 Without using a calculator, give the exact trigonometric function value with rational denominator. 7) sin 60 7) A) 1 B) C) D) Solve the problem. 8) In one area, the lowest angle of elevation of the sun in winter is 1 4. A fence is to be built 1. ft away from a plant in the direction of the sun. (See drawing) Find the maximum height, x, for the fence so that the plant will get full sun. Round your answer to the tenths place when necessary. 8) 1 4 1. ft A) 4.6 ft B) 6.8 ft C) 5.6 ft D) 5. ft 6
9) Find a formula for the area of the figure in terms of s. 9) A) 6 4 s B) s C) 6 s D) 6 s 0) Any offset between a stationary radar gun and a moving target creates a "cosine effect" that reduces the radar mileage reading by the cosine of the angle between the gun and the vehicle. That is, the radar speed reading is the product of the actual reading and the cosine of the angle. Find the radar reading to the nearest hundredth for the auto shown in the figure. 0) 1 angle Actual speed: 8 mph A) 8.86 mph B) 71.14 mph C) 8.14 mph D) 4.75 mph Use a calculator to decide whether the statement is true or false. 1) sin (45 + 10 ) = sin 45 + sin 10 1) A) True B) False Find all values of, if is in the interval [0, 60 ) and has the given function value. ) tan = 1 ) A) 45 and 15 B) 5 and 15 C) 15 and 5 D) 45 and 5 Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle. ) cos 48 ) A) sec 4 B) cos 18 C) sin 4 D) sin 48 Find the exact value of the expression. 4) cos 0 4) A) B) C) D) Solve the problem. 5) The angle of elevation from a point on the ground to the top of a tower is 5 16. The angle of elevation from a point 10 feet farther back from the tower is 4 18. Find the height of the tower. Round to the nearest foot. A) 164 ft B) 17 ft C) 16 ft D) 158 ft 5) 7
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. 6) Find sin A when a = 7 and b = 6. 6) A) 85 6 B) 6 85 85 C) 85 7 D) 7 85 85 Find all values of, if is in the interval [0, 60 ) and has the given function value. 7) cos = A) 5 and 15 B) 0 and 0 C) 15 and 5 D) 45 and 5 7) Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. 8) sec 57 1 8) A).750186 B) 1.86009 C) 1.861009 D).740186 Solve the problem for the given information. 9) Find the equation of a line passing through the origin and making a 45 angle with the positive x-axis. A) y = x B) y = x C) y = x D) y = -x 9) Find a solution for the equation. Assume that all angles are acute angles. 40) tan( + ) = cot( + 6 ) 40) A) 5.5 B) C) 6 D) 9.5 Find the exact value of the expression. 41) sin 115 41) A) - B) - 1 C) D) - Without using a calculator, give the exact trigonometric function value with rational denominator. 4) tan 45 4) A) 1 B) 1 C) D) Solve the problem. 4) The grade resistance F of a car traveling up or down a hill is modeled by the equation F = W sin, where W is the weight of the car and is the angle of the hill's grade ( > 0 for uphill travel, < 0 for downhill travel). What is the grade resistance (to the nearest pound) of a 050-lb car on a level road ( = 0 )? A) -050 lb B) 0 lb C) undefined D) 050 lb 4) 8
44) A 5.-ft fence is 11.46 ft away from a plant in the direction of the sun. It is observed that the shadow of the fence extends exactly to the bottom of the plant. (See drawing) Find, the angle of elevation of the sun at that time. Round the measure of the angle to the nearest tenth of a degree when necessary. 44) 5. ft 11.46 ft A) = 5.8 B) = 4.6 C) = 4.4 D) = 4. 45) A center-pivot irrigation system waters a sector-shaped field. Find the area of the field if the central angle, = 5 and the radius, r = 150 meters. Round to the nearest whole number. A) 46 m B) 9 m C) 1,744 m D) 687 m 45) Find the area of a sector of a circle having radius r and central angle. If necessary, express the answer to the nearest tenth. 46) r = 16.0 m, = 0 46) A) 89.4 m B) 44.7 m C).8m D) 0.5m Solve the problem. 47) Find for a spoke on a bike tire revolving 85 times per minute. 47) A) 170 radians per min B) 85 radians per min C) 85 radians per min D) radians per min 170 9
The figure shows an angle in standard position with its terminal side intersecting the unit circle. Evaluate the indicated circular function value of. 48) Find sin. 48) 7 5, - 4 5 A) - 7 4 B) - 4 5 C) 4 5 D) 7 5 Solve the problem. 49) A circular sector has an area of 16 in and an arc length of 6 inches. What is the measure of the central angle in degrees? Round to the nearest degree. A) B) 19 C) 64 D) 11 49) Find the value of s in the interval [0, /] that makes the statement true. Round to four decimal places. 50) sin s = 0.8065 50) A) -0.7966 B) 0.98 C) 0.450 D).04 Use the formula s = r t to find the value of the missing variable. Give an exact answer. 51) r = 4 cm, = 9 radian per sec, t = 4 sec 51) A) 16 9 cm B) 16 9 cm C) 9 16 cm D) 9 16 cm For the given value of s, decide in which quadrant an angle of s radians lies by evaluating sin s and cos s. 5) s = 5 5) A) I B) II C) IV D) III 10
Find the corresponding angle measure in radians. 5) 10 5) A) 6 B) C) D) 6 Use the formula v = r to find the value of the missing variable. Give an exact answer unless otherwise indicated. 54) v = 19 ft per sec, r = 9.7 ft (Round to four decimal places when necessary.) 54) A) 1.9588 radians per sec B) 0.9 radian per sec C) 0.5105 radian per sec D) 6.0479 radians per sec Find the value of s in the interval [0, /] that makes the statement true. Round to four decimal places. 55) tan s =.848 55) A) 1.0505 B) 4.74 C) 1.7 D) 0.805 Solve the problem. 56) Find the measure (in radians) of a central angle of a sector of area 46 square inches in a circle of radius 5 inches. Round to the nearest hundredth. A) 1.84 radians B) 5.5 radians C) 7.6 radians D).68 radians 56) Decide whether the statement is possible or impossible for an angle. 57) sec = -0.41 57) A) Impossible B) Possible The triangles are similar. Find the angle or side that corresponds to the given angle or side in the other triangle. 58) AC 58) (AB is parallel to DE.) A) Cannot be determined B) DE C) EC D) CD 11
The triangles are similar. Find the missing side, angle or value of the variable. 59) x 59) a = 5 b = 75 c = 5 A) x = 9 B) x = 5 C) x = 1 D) x = 6 Use the fundamental identities to find the value of the trigonometric function. 60) Find csc, given that cot = - 9 8 and cos < 0. 60) A) - 145 9 B) 9 145 145 C) 145 8 D) - 9 145 145 The triangles are similar. Find the angle or side that corresponds to the given angle or side in the other triangle. 61) AC 61) A) RT B) Cannot be determined C) ST D) RS Evaluate the expression. 6) cos 0-8 sin 90 6) A) 0 B) -8 C) 1 D) -7 6) tan(-540) 6) A) -1 B) Undefined C) 1 D) 0 1
Sketch an angle in standard position such that has the least positive measure and the given point is on the terminal side of. 64) (, -6) 64) A) B) C) D) Solve the problem for the given information. 65) 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. 65) A) y = x B) y = x C) y = x D) y = x Decide whether the statement is true or false. 66) cos 7 cos 59 66) A) True B) False Determine whether the statement is true or false. 67) cos 60 = cos 180 - cos 10 67) A) True B) False 1
Solve the problem. 68) Find the exact value of x in the figure. 68) 14 x A) 7 B) 7 6 C) 14 6 D) 14 Find the sign of the following. 69) cot ( + 180 ), given that is in the interval (90, 180 ). 69) A) negative B) positive Convert the radian measure to degrees. Give answer using decimal degrees to the nearest hundredth. Use.1416 for. 70) 1.6816 70) A) 96.85 B) 96.5 C) 95.65 D) 97.5 Solve the problem. 71) A pulley rotates through 51 in one minute. How many rotations (to the nearest tenth of a rotation) does the pulley make in an hour? A) 06.0 rotations B) 8.5 rotations C) 17.0 rotations D) 15.0 rotations 71) Find the exact circular function value. 7) cos - 7) A) - B) - 1 C) D) undefined The triangles are similar. Find the angle or side that corresponds to the given angle or side in the other triangle. 7) B 7) A) S B) T C) R D) C Provide an appropriate response. 74) Find the complement of an angle whose measure is 8 18. 74) A) 5 4 B) 5 41 C) 51 18 D) 51 4 14
Solve the problem. 75) A tunnel is to be dug from point A to point B. Both A and B are visible from point C. If AC is 0 miles and BC is 547 miles, and if angle C is 90, find the measure of angle B. Round your answer to the tenths place. A) 4.1 B) 1.9 C) 18.7 D) 1.4 75) Determine whether the statement is true or false. 76) cos 540 = 1 - sin 70 76) A) True B) False Convert the degree measure to radians. Leave answer as a multiple of. 77) -0 77) A) - 7 B) - 5 C) - 6 D) - 8 Evaluate the expression. 78) tan(-180 ) 78) A) -1 B) 0 C) 1 D) Undefined Find the exact value of the expression. 79) csc (-40 ) 79) A) B) C) - D) - Solve the problem. 80) Electrical wire is being wound around a drum with radius of 0.95 meters. How much line (to the nearest hundredth of a meter) would be wound around the drum if it is rotated through an angle of 40.8? A) 5.55 m B) 5.75 m C) 5.45 m D) 5.65 m 80) 15
Answer Key Testname: PRACTICE1TRIG 1) A ) C ) B 4) D 5) C 6) A 7) A 8) C 9) A 10) B 11) D 1) C 1) C 14) D 15) B 16) B 17) C 18) B 19) B 0) B 1) A ) D ) D 4) B 5) A 6) C 7) B 8) D 9) D 0) B 1) B ) D ) C 4) D 5) C 6) D 7) B 8) B 9) C 40) A 41) A 4) A 4) B 44) C 45) D 46) B 47) A 48) B 49) C 50) B 16
Answer Key Testname: PRACTICE1TRIG 51) A 5) B 5) C 54) A 55) C 56) D 57) A 58) C 59) A 60) C 61) D 6) D 6) D 64) B 65) C 66) A 67) B 68) C 69) A 70) B 71) B 7) B 7) B 74) D 75) B 76) A 77) C 78) B 79) A 80) D 17