FLEX Mathematics Introduction to Trigonometry Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Evaluate the expression. 1) 8 tan 0 + 3 csc 20 1) A) Undefined B) 0 C) 3 D) -3 Solve the problem. Round answers to the nearest tenth if necessary. 2) A triangle drawn on a map has sides of lengths cm, cm, and 15 cm. The shortest of the corresponding real-life distances is 92 km. Find the longest of the real-life distances. A) 20.1 km B) 134.6 km C) 19.1 km D) 144.6 km 2) 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. 3) tan, given that cot = A) 4 4 B) C) 4 D) 4 3) Solve the problem. 4) A surveyor recording data for a new subdivision measured an angle as.. The next day, a different surveyor measured the same angle as 31. Find the difference between these measurements (i) to the nearest minute and (ii) to the nearest hundredth of a degree. A) (i) (ii) 1.29 B) (i) 46 (ii) 0.46 C) (i) 15 (ii) 0.25 D) (i) 38 (ii) 0.43 4) Use the fundamental identities to find the value of the trigonometric function. 5) Find csc, given that cot = - 2 and cos < 0. 5) A) 53 53 B) - 53 C) - 53 53 D) 53 2 Use the properties of angle measures to find the measure of each marked angle. 6) 6) a = (2x + 8) b = (4x - 62) A) 35, 35 B) 55, 55 C) -16, -16 D) 8, 8 The triangles are similar. Find the angle or side that corresponds to the given angle or side in the other triangle. ) B ) A) C B) S C) R D) T 1
Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene. 8) 8) A) Acute, scalene B) Right, scalene C) Obtuse, equilateral D) Obtuse, scalene 9) 9) A) Right, scalene B) Obtuse, equilateral C) Obtuse, scalene D) Acute, equilateral Decide whether the statement is possible or impossible for an angle. 10) sec = 0.9 10) A) Possible B) Impossible Give an expression that generates all angles coterminal with the given angle. Let n represent any integer. ) -180 ) A) -180 + n 180 B) -180 + n 360 C) -180 - n 180 D) -180 + 2n 360 2
Sketch an angle in standard position such that has the least positive measure and the given point is on the terminal side of. 12) (-2, -) 12) A) B) C) D) The triangles are similar. Find the missing side, angle or value of the variable. 13) 13) a = 13 b = 12 c = 5 d = 26 e = 24 A) x = B) x = 10 C) x = 5 D) x = 15 3
Use the fundamental identities to find the value of the trigonometric function. 14) Find csc, given that sin = - 2 3 and is in quadrant IV. 14) A) 3 B) - 9 C) 5 4 D) - 3 2 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. 15) 295 15) A) 55 and -105 B) 655 and -65 C) 85 and -95 D) 65 and -65 Suppose that is in standard position and the given point is on the terminal side of. Give the exact value of the indicated trig function for. 16) (12, 16); Find sin. 16) A) 3 5 B) 4 3 C) 4 5 D) 3 4 Find the measure of each angle in the problem. 1) Supplementary angles with measures 2x + and 3x - 2 degrees 1) A) 5 and 123 B) and 103 C) 6 and 3 D) 8 and 93 Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene. 18) 18) A) Obtuse, isosceles B) Obtuse, equilateral C) Acute, scalene D) Right, isosceles 4
Find the angle of least positive measure coterminal with the given angle. 19) -6 19) A) B) 6 C) 424 D) 244 An equation of the terminal side of an angle in standard position is given along with a restriction on x. Find the indicated trigonometric function value of. Do not use a calculator. 20) 2x + 3y = 0, x 0; Find csc. 20) A) 3 B) - 2 13 C) D) - 3 2 3 2 2 Provide an appropriate response. 21) Find the complement of an angle whose measure is 33 21. 21) A) 5 39 B) 56 39 C) 56 21 D) 5 38 Place your graphing calculator in parametric and degree modes. Set the window for Tmin=0, Tmax=360, Tstep=1, Xmin= -1.8, Xmax=1.8, Xscl=1, Ymin= -1.2, Ymax=1.2, Yscl=1. Set the functions to X1T=cos T, Y1T=sin T. Graph the circle of radius 1 on the screen. Use the trace feature to move a short distance around the circle. 22) For what angle T is cos T 0.66? (Assume 0 T 90.) 22) A) 40 B) 36.832 C) 0.66 D) 50 5
Sketch an angle in standard position such that has the least positive measure and the given point is on the terminal side of. 23) (3, 6) 23) A) B) C) D) 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. 24) III, r x 24) A) Positive B) Negative 6
Solve the problem. Round answers to the nearest tenth if necessary. 25) Two quadrilaterals (four-sided figures) are similar. The lengths of the three longest sides of the first quadrilateral are 24 ft, 16 ft, and 12 ft. The lengths of the two shortest sides of the second quadrilateral are 18 ft and 9 ft. Find the unknown lengths of the sides of these two figures. A) Not enough information is provided. B) The unknown side in the first quadrilateral is 6 ft. The two unknown sides in the second quadrilateral are 36 ft and 24 ft. C) The unknown side in the first quadrilateral is 8 ft. The two unknown sides in the second quadrilateral are 36 ft and 12 ft. D) The unknown side in the first quadrilateral is 10 ft. The two unknown sides in the second quadrilateral are 2 ft and 24 ft. 25) 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. 26) csc, given that sin = A) 6 6 B) C) 6 D) 6 26) Perform the calculation. 2) 90-34 28 50 2) A) 56 32 10 B) 55 31 9 C) 55 31 10 D) 55 32 10 The triangles are similar. Find the angle or side that corresponds to the given angle or side in the other triangle. 28) AC 28) A) RT B) Cannot be determined C) ST D) RS 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. 29) cot(n 180 ) 29) A) Undefined B) 1 C) 0 D) -1
Sketch an angle in standard position such that has the least positive measure and the given point is on the terminal side of. 30) (3, -6) 30) A) B) C) D) Perform the calculation. 31) 29 39 + 139 38 31) A) 419 1 B) 18 C) 18 1 D) 419 8
Sketch an angle in standard position such that has the least positive measure and the given point is on the terminal side of. 32) (6, 2) 32) A) B) C) D) Solve the problem. 33) A wheel is rotating 240 times per minute. Through how many degrees does a point on the edge of the wheel move in 1 2 seconds? 33) A) 540 B) 20 C) 24 D) 180 9
The triangles are similar. Find the missing side, angle or value of the variable. 34) B 34) a = cm b = 65 A) cm B) 85 C) 30 D) 65 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. 35) II, x y 35) A) Positive B) Negative 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. 36) -85 36) A) 15 and -5 B) 25 and -445 C) 185 and -355 D) 85 and -105 Convert the angle to degrees, minutes, and seconds. 3) 153.38 3) A) 153 20 38 B) 153 23 48 C) 153 22 38 D) 153 22 48 Find the measure of the third angle of a triangle if the measures of the other two angles are given. 38) 102.5 and 42.4 38) A) 45.1 B) 215.1 C) 35.1 D) 55.1 10
Use the fundamental identities to find the value of the trigonometric function. 39) Find cot, given that tan = and is in quadrant III. 39) 3 A) - 3 2 B) 3 C) - 9 D) 5 4 Place your graphing calculator in parametric and degree modes. Set the window for Tmin=0, Tmax=360, Tstep=1, Xmin= -1.8, Xmax=1.8, Xscl=1, Ymin= -1.2, Ymax=1.2, Yscl=1. Set the functions to X1T=cos T, Y1T=sin T. Graph the circle of radius 1 on the screen. Use the trace feature to move a short distance around the circle. 40) For what angle T is sin T 0.54? (Assume 0 T 90.) 40) A) 55 B) 0.54 C) 46.91 D) 35 The triangles are similar. Find the angle or side that corresponds to the given angle or side in the other triangle. 41) C 41) A) C B) T C) R D) S 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. 42) II, r x 42) A) Positive B) Negative Use the properties of angle measures to find the measure of each marked angle. 43) Lines m and n are parallel. 43) a = (2x + 66) b = (4x + 8) A) 151, 151 B) 64, 64 C) 29, 29 D) 124, 124 Identify the quadrant for the angle satisfying the following conditions. 44) cot > 0 and sin < 0 44) A) Quadrant II B) Quadrant III C) Quadrant IV D) Quadrant I 45) cos < 0 and csc < 0 45) A) Quadrant II B) Quadrant IV C) Quadrant III D) Quadrant I 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. 46) tan((2n + 1) 90 ) 46) A) 1 B) 0 C) Undefined D) -1
Use the fundamental identities to find the value of the trigonometric function. 4) Find cos, given that sin = - 5 and is in quadrant III. 4) 13 A) 12 5 B) - 5 12 C) - 13 5 D) - 12 13 Provide an appropriate response. 48) Find the complement of an angle whose measure is 3 10 50. 48) A) 52 50 10 B) 53 50 10 C) 52 49 9 D) 52 49 10 Give an expression that generates all angles coterminal with the given angle. Let n represent any integer. 49) 98 49) A) 98 + n 90 B) 98 + n 360 C) 98 + n 180 D) 98 + n 20 Use the fundamental identities to find the value of the trigonometric function. 50) Find sec, given that tan = 2.444 and is in quadrant I. 50) A) 1.9358402 B) 2.9238044 C) -2.9238044 D) -1.9358402 12
Answer Key Testname: TRIGONOMETRY 1 1) D 2) C 3) A 4) C 5) D 6) D ) D 8) B 9) C 10) B ) B 12) B 13) B 14) D 15) B 16) C 1) B 18) A 19) D 20) C 21) B 22) A 23) A 24) B 25) B 26) A 2) C 28) D 29) A 30) D 31) A 32) D 33) B 34) D 35) B 36) B 3) D 38) C 39) B 40) D 41) C 42) B 43) D 44) B 45) C 46) C 4) D 48) D 49) B 50) B 13