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

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1 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 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. 1) 115 1) A) 295 and -65 B) 475 and -245 C) 475 and -245 D) 295 and -65 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. 2) (0, -9); Find csc θ. 2) A) -9 B) -1 C) 9 D) 1 Use the properties of angle measures to find the measure of each marked angle. 3) 3) a = (2x + 5) b = (4x - 33) A) -21, -21 B) 43, 43 C) 19, 19 D) 71, 71 Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene. 4) 4) A) Acute, equilateral B) Obtuse, scalene C) Right, scalene D) Obtuse, equilateral 1

2 Use the properties of angle measures to find the measure of each marked angle. 5) Lines m and n are parallel. 5) a = (3x + 9) b = (2x + 76) A) 18, 161 B) 19, 161 C) 66, 114 D) 71, 109 Convert the angle to degrees, minutes, and seconds. 6) A) B) C) D) ) The triangles are similar. Find the missing side, angle or value of the variable. 7) R 7) a = 18 cm b = 118 A) 52 B) 118 C) 18 cm D) 10 Provide an appropriate response. 8) Find the complement of an angle whose measure is A) B) C) D) ) Decide whether the statement is possible or impossible for an angle θ. 9) cos θ = 5 7 and sec θ = 7 5 9) A) Possible B) Impossible Identify the quadrant for the angle θ satisfying the following conditions. 10) sec θ < 0 and tan θ < 0 A) Quadrant IV B) Quadrant III C) Quadrant II D) Quadrant I 10) An equation of the terminal side of an angle θ in standard position is given along with a restriction on x. Find the indicated trigonometric function value of θ. Do not use a calculator. 11) -6x - 5y = 0, x 0; Find sec θ. 11) A) B) C) D)

3 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. 12) (21, 28); Find sin θ. 12) A) 4 3 B) 4 5 C) 3 4 D) 3 5 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. 13) (-2, 5) 13) y x A) B) C) D) 3

4 The triangles are similar. Find the missing side, angle or value of the variable. 14) 14) a = 6 b = 8 c = 5 d = 3 e = 4 A) x = 15 B) x = 11 C) x = 10 D) x = 5 Evaluate the expression. 15) 9 tan sin csc2 270 A) 5 B) 14 C) 0 D) -5 15) 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. 16) II, y x 16) A) Positive B) Negative Find the measure of the third angle of a triangle if the measures of the other two angles are given. 17) 10 and 90 A) 100 B) -10 C) 260 D) 80 17) Use the fundamental identities to find the value of the trigonometric function. 18) Find sin θ, given that cos θ = 4 7 and tan θ < 0. 18) A) B) C) D) - 33 Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene. 19) 19) A) Acute, scalene B) Obtuse, scalene C) Obtuse, equilateral D) Acute, isosceles 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. 20) IV, x y 20) A) Positive B) Negative 4

5 The triangles are similar. Find the missing side, angle or value of the variable. 21) C. 21) m A = 63 m E = 35 A) 63 B) 35 C) 92 D) 82 Perform the calculation. 22) A) B) C) D) ) Evaluate the expression. 23) sin ) A) 0 B) Undefined C) -1 D) 1 2 Identify the quadrant for the angle θ satisfying the following conditions. 24) csc θ > 0 and sec θ > 0 A) Quadrant I B) Quadrant II C) Quadrant IV D) Quadrant III 24) The triangles are similar. Find the missing side, angle or value of the variable. 25) 25) a = 14 b = 21 c = 10 d = 15 e = 20 A) x = 26 B) x = 20 C) x = 28 D) x = 35 Solve the problem. Round answers to the nearest tenth if necessary. 26) A tree casts a shadow 16 m long. At the same time, the shadow cast by a 62-centimeter-tall statue is 93 cm long. Find the height of the tree. A) 22.5 m B) 9.2 m C) 10.7 m D) 24.0 m 26) 5

6 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. 27) III, x y 27) A) Negative B) Positive 28) II, x y 28) A) Negative B) Positive 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. 29) ) A) 350 and -10 B) 530 and -190 C) 350 and -10 D) 530 and -190 If n is an integer, n 180 represents an integer multiple of 180, and (2n + 1) 90 represents an odd integer multiple of 90. Decide whether the expression is equal to 0, 1, -1, or is undefined. 30) cot(n 180 ) 30) A) -1 B) Undefined C) 1 D) 0 Find the angle of least positive measure coterminal with the given angle. 31) 500 A) 250 B) 130 C) 320 D) ) Use the fundamental identities to find the value of the trigonometric function. 32) Find sin θ, given that cos θ = 2 3 and θ is in quadrant IV. 32) A) B) C) 5 4 D) Determine the signs of the given trigonometric functions of an angle in standard position with the given measure. 33) sec (-35 ) and sin (-35 ) 33) A) negative and negative B) positive and positive C) positive and negative D) negative and positive Give an expression that generates all angles coterminal with the given angle. Let n represent any integer. 34) 179 A) n 90 B) n 180 C) n 720 D) n ) Convert the angle to decimal degrees and round to the nearest hundredth of a degree. 35) A) B) C) D) ) 6

7 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. 36) (18, 24); Find csc θ. 36) A) 5 4 B) 5 3 C) 4 3 D) 3 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. 37) tan θ, given that cot θ = ) A) 13 7 B) C) D) 7 6 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. 38) IV, r y 38) A) Negative B) Positive 7

8 Answer Key Testname: REVIEW TRIGONOMETRY TEST 1 1) C 2) B 3) B 4) B 5) C 6) D 7) B 8) D 9) A 10) C 11) D 12) B 13) B 14) C 15) A 16) B 17) D 18) C 19) D 20) B 21) D 22) C 23) C 24) A 25) C 26) C 27) B 28) A 29) B 30) B 31) D 32) B 33) C 34) D 35) A 36) A 37) B 38) A 8