H Intro to Cal Final Exam Review Spring 13.tst

Name__________________________________________H INTRO TO CALCULUSFinal Exam Review Packet -- Spring 2013MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.1) Find the reference angle for the given angle- 13π12A) 11π12B) 13π12C) π 12D) π 242) A point on the terminal side of angle θ is given. Find the exact value of the indicated trig. function of θ.(12, 16) Find csc θ.A) 4 3B) 3 4C) 5 3D) 5 43) Graph the function.y = 3 sec xA)B)10y-2 - 8642-2-4-6 2-8xy-2 - 8642x-2 2-4-6-8C)-10D)8y8y664422-2 - x-2 2-4-6-8-2 - x-2 2-4-6-81

4) Use an identity to find the value of the expression. Do not use a calculator.sin 1.7 csc 1.7A) -1 B) -1.7 C) 1.7 D) 15) Graph the function.y = 3 4 sin (x - π 4 )A)B)yy33--22x--22x-3-3C)D)yy33--22x--22x-3-36) Determine the phase shift of the function.y = 1 4sin (4x + π)A) π 4 units to the right B) - π 4units to the leftC) π units to the left D) π 4units to the left7) The point P on the unit circle that corresponds to a real number t is given. Find the values of the indicatedtrigonometric function at t.38 , 55Find sin t.8A) 3 8B)558C)553D) 3 55552

8) Find the reference angle for the given angle.-229°A) 131° B) 49° C) 139° D) 41°9) Sin t and cos t are given. Use identities to find the indicated value. Where necessary, rationalize denominators.sin t =A) 5 1111116 , cos t = 5 . Find sec t.6B) 6 1111C) 6 5D)11510) Find the reference angle for the given angle.96°A) 6° B) 16° C) 84° D) 94°11) Find the exact value of the expression.3sin-12A) π 3B) π 4C) 3π 4D) 2π 312) Graph the function and y = sin x in the same rectangular system for 0 ≤ x ≤ 2π.y = 2 sin xA)B)4321y4321y-12x-12x-2-2-3-3-4-4C)D)4y4y332211-12x-12x-2-2-3-3-4-43

13) Find the exact value of the indicated trigonometric function of θ.cos θ = 1517 , 3π< θ < 2π Find cot θ.2A) - 158B) - 8 15C) - 15 22D) 1715Use the given triangles to evaluate the expression. Rationalize all denominators.14) cot 45°A) 1 B) 2 3C) 2 D)32215) 83Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function ofthe given angle. Give an exact answer with a rational denominator.Find tan θ.A) tan θ = 8 3B) tan θ = 3 8C) tan θ =738D) tan θ =73316) A point on the terminal side of angle θ is given. Find the exact value of the indicated trig. function of θ.(-20, 48) Find sin θ.A) - 12B) 125C)D) - 5 1313131317) Determine the amplitude or period as requested.Period of y = 5 sin 3x - π 2A) 3 2B) 3π 2C) 2π 3D) 2 34

18) The point P on the unit circle that corresponds to a real number t is given. Find the values of the indicatedtrigonometric function at t.29 , - 77Find csc t.9A)772B)779C) -779D) - 9 777719) Find the exact value of the trigonometric function. Do not use a calculator.tan - 5π 4A) -1 B) -22C) - 2 D) 120) Find the reference angle for the given angle.436°A) 104° B) 76° C) 14° D) 166°21) A point on the terminal side of angle θ is given. Find the exact value of the indicated trig. function of θ.(4, -2) Find sin θ.A) -55B) -2 C)52D) 2 5522) Use the given triangles to evaluate the expression. Rationalize all denominators.tan π 6 - sin π 3A) 2 3 - 3 26B) -62C) -36D) 323) Determine the phase shift of the function.y = 4 sin (4x - π 2 )A) π 2units to the left B) 4π units downC) π 8units to the right D) 4π units up5

24) Find the exact value of the expression.cos-1 (-1)A) 0 B) 2π C) π D) π 225) Find the exact value of the indicated trigonometric function of θ.csc θ = - 5 , θ in quadrant III Find cot θ.2A) - 5 2121B)212C) - 2 2121D) -21526) Classify the angle as acute, right, obtuse, or straight.A) right B) acute C) straight D) obtuse27) Graph the function.y = 2 sec x + π 2A)B)8y8y664422- -2x- -2x-4-4-6-6-8-8C)D)8y8y664422- -2x- -2x-4-4-6-6-8-86

28) Use an identity to find the value of the expression. Do not use a calculator.sin2 π 3 + cos 2 π 3A) -1 B) 1 C) - π 3D) π 329) Find a positive angle less than 360° that is coterminal with the given angle.484°A) 124° B) 114° C) 304° D) 242°30) A point on the terminal side of angle θ is given. Find the exact value of the indicated trig. function of θ.(9, 12) Find cos θ.A) 4 3B) 4 5C) 3 5D) 3 431) Graph the function.y = 2 tan 4xA)B)yy4422-2-22x-2-22x-4-4C)D)yy4422-2-22x-2-22x-4-432) Find the exact value of the indicated trigonometric function of θ.cot θ = - 7 , cos θ < 0 Find csc θ.2A)532B) 7 5353C) -537D) - 7 53537

33) Determine the amplitude or period as requested.Period of y = 7 8 cos 8π 5 xA) 5 4B) 4 7C) 7π 4D) 16π534) The given angle is in standard position. Determine the quadrant in which the angle lies.262°A) Quadrant I B) Quadrant III C) Quadrant IV D) Quadrant II35) Graph the function.y = 1 3 cot xA)B)3y3y--22x--22x-3-3C)D)3y3y--22x--22x-3-336) Find the exact value of the expression.3cos-12A) 11π6B) π 4C) 7π 4D) π 637) The given angle is in standard position. Determine the quadrant in which the angle lies.139°A) Quadrant III B) Quadrant I C) Quadrant IV D) Quadrant II8

38) Find the reference angle for the given angle.- 3π 4A) 5π 4B) 3π 4C) π 8D) π 439) Graph the function.y = - 3 4 cos (2x + π 4 )A)B)yy33--22x--22x-3-3C)D)yy33--22x--22x-3-340) The point P on the unit circle that corresponds to a real number t is given. Find the values of the indicatedtrigonometric function at t.29 , 77Find tan t.9A) 2 7777B)779C)772D) 9 241) Solve the equation on the interval [0, 2π).sin2 x - cos2 x = 0A) π 4B) π 4 , π 6C) π 4 , 3π 4 , 5π 4 , 7π 4D) π 4 , π 39

42) Complete the identity.(sec x + 1)(sec x - 1)= ?tan2 xA) 2 B) 1 C) -1 D) 043) Use the given triangles to evaluate the expression. Rationalize all denominators.sin π 6 csc π 6 - cot π 6A) 1 - 3 B) 2 - 32C) 3 - 33D) 2 - 344) Complete the identity.cos (2π - x) = ?A) cos x B) sin x C) -sin x D) -cos x45) Write the expression as the cosine of an angle, knowing that the expression is the right side of the formula forcos (α - β) with particular values for α and β.cos 2π πcos9 18 + sin 2π πsin9 18A) cos ( 5π 6 ) B) cos ( π 6 ) C) cos ( 2π 3 ) D) cos ( π 3 )46) Complete the identity.tan x(cot x - cos x) = ?A) 1 - sin x B) 0 C) 1 D) - sec2 x47) Solve the equation on the interval [0, 2π).sin x - 2 sin x cos x = 0A) π 3 , 5π 3B) 0, π 3 , π, 5π 3C) π 3 , π, 5π 3 , 2π D) π 3 , 5π 3 , 2π10

48) Use the given information to find the exact value of the expression.Find tan 2θ. sin θ = 4 , θ lies in quadrant II.5A) - 9 7B) 2425C) 247D) - 24749) Graph the function.y = tan xA)yB)y2211--22322523x--22322523x-1-1-2-2C)D)yy2211--22322523x--22322523x-1-1-2-250)51312Use the figure to find the exact value of the trigonometric function.Find cos 2θ.A) 118169B) - 119169C) 119169D) 12016911

51) Find the exact value of the expression.cos 5π12 sin π 4 - cos π 5πsin4 12A) 1 4B) 1 2C)32D) 152) Solve the equation on the interval [0, 2π).cos2 x + 2 cos x + 1 = 0A) π 4 , 7π B) π 42 , 3π 2C) π D) 2π53) Use the given information to find the exact value of the expression.Find cos 2θ. sin θ = 7 , θ lies in quadrant I.25A) 336625B) 528625C) - 527625D) 52762554) Solve the equation on the interval [0, 2π).cos x = sin xA) π 4 , 7π 4B) π 4 , 5π 4C) 3π 4 , 7π 2D) 3π 4 , 5π 455) Solve the equation on the interval [0, 2π).cos 2x =32A) π 2C) π 6 , 11π6B) 3π 2D) π 12 , 11π12 , 13π12 , 23π1256) Solve the equation on the interval [0, 2π).2 cos2 x + sin x - 2 = 0A) π 6 , 5π 6B) π 3 , 2π 3C) π 2 , 3π 2 , π 3 , 2π 3D) 0, π, π 6 , 5π 657) Complete the identity.(cot x + 1)(cot x + 1) - csc2 x= ?cot xA) 1 B) 0 C) 2 D) cot x58) Use substitution to determine whether the given x-value is a solution of the equation.cos x + 1 = sin x, x = 5π 4A) Yes B) No12

59) Complete the identity.sin (α + β) sin (α - β) = ?A) sin2 β - sin2 α B) cos2 β - cos2 α C) cos2 β + cos2 α D) sin2 α - cos2 β60) Use substitution to determine whether the given x-value is a solution of the equation.3tan x =3 , x = 7π 6A) Yes B) No61) Solve the equation on the interval [0, 2π).cos 2x = 2 - cos 2xA) π 8 , 7π 8 , 9π 8 , 15π B) π 84 , 3π 4 , 5π 4 , 7π 4C) 0, 2π 3 , π, 4π 3D) no solution62) Complete the identity.sin x - cos x cos x - sin x+ = ?sin x cos xA) 1 - sec x csc x B) sec x csc x C) 2 + sec x csc x D) 2 - sec x csc x63) Use trigonometric identities to find the exact value.tan 50° + tan 100°1 - tan 50° tan 100°A) - 1 2B) -2 C) - 3 D) -3364) Complete the identity.csc x(sin x + cos x) = ?A) 1 + cot x B) -2 tan2 x C) sin x tan x D) sec x csc x65) Find all solutions of the equation.2 cos x + 2 = 0A) x = π 4 + nπ or x = 7π 4 + nπ B) x = 3π 4 + 2nπ or x = 5π 4 + 2nπC) x = π 4 + 2nπ or x = 7π 4 + 2nπ D) x = 3π 4 + nπ or x = 5π 4 + nπ66) Find the exact value by using a difference identity.tan 105°A) 2 + 3 B) 2 + 34C) 2 - 34D) -2 - 367) Use the given information to find the exact value of the expression.Find cos (α + β). sin α = 4 12, α lies in quadrant I, and cos β = , β lies in quadrant I.5 13A) 5665B) 6365C) 1665D) 336513

68) Find the exact value of the expression.sin 255° cos 15° - cos 255° sin 15°A) - 1 2B) -32C) 174D)3269) Use the given information to find the exact value of the expression.Find cos (α - β). sin α = 7 25 , α lies in quadrant II, and cos β = 2 , β lies in quadrant I.5A)48 - 7 21125B)14 - 24 21125C)14 + 24 21125D)-48 + 7 2112570) Determine the amplitude or period as requested.Period of y = -2 sin 6πxA) 6π B) 1 3C) 3 D) π 371) Convert the angle in degrees to radians. Express answer as a multiple of π.-90°A) - π 3 radians B) - π 4 radians C) - π 2 radians D) - π 8 radians72) Use the given triangles to evaluate the expression. Rationalize all denominators .cos π 6A)22B) 3 C) 2 33D)3273) The point P on the unit circle that corresponds to a real number t is given. Find the values of the indicatedtrigonometric function at t.47 , - 33Find cos t.7A) 4 7B) - 4 7C) -337D)33714

74) Find the exact value of the indicated trigonometric function of θ.tan θ = - 8 , θ in quadrant II Find cos θ.3A)738B) 3 7373C) - 3 7373D) -73375) Use the graph to obtain the graph of the reciprocal function. Give the equation of the function for the graphthat you obtain.y = 1 2 sin 1 2 xA) y = 1 2 csc 1 2 x xy1B) y = 1 2 csc 2x xy1-2 2x-2 2x-1-1C) y = 1 2 sec 1 2 x xy1D) y = 1 2 sec 2x xy1-2 2x-2 2x-1-176) Determine the amplitude or period as requested.Amplitude of y = 4 sin 1 3 xA) 4π 3B) 4 C) π 4D) 6π77) Find the exact value of the expression.sin-1 1A) π 4B) π 3C) π D) π 215

78) Find the exact value of the expression.tan-1 0A) π B) π 2C) 2π D) 079) Graph the function.y = tan xA)yB)y2211--22322523x--22322523x-1-1-2-2C)D)yy2211--22322523x--22322523x-1-1-2-216

80) Graph the function.y = -cot xA)yB)y2211--22322523x--22322523x-1-1-2-2C)D)yy2211--22322523x--22322523x-1-1-2-281) Convert the angle in radians to degrees.9π4A) 80π° B) 810° C) 160° D) 405°82) Find the exact value under the given conditions.cos α = - 7 25 , π 2 < α < π; sin β = - 215 , π < β < 3π 2Find tan (α + β).A)-48 + 7 2114 + 24 21B)48 - 7 2114 + 24 21C)14 + 24 21-48 + 7 21D)-48 + 7 2112583) Solve the equation on the interval [0, 2π).cos 2x =22A) π 4 , 3π 4 , 5π 4 , 7π 4B) 0, 2π 3 , π, 4π 3C) π 8 , 7π 8 , 9π 8 , 15π8D) no solution17

84) Graph the function and y = cos x in the same rectangular system for 0 ≤ x ≤ 2π.y = 1 4 cos xA)B)4y4y332211-12x-12x-2-2-3-3-4-4C)D)4y4y332211-12x-12x-2-2-3-3-4-485) Find the exact value under the given conditions.sin α = 3 5 , 0 < α < π 20; cos β =2 29 , 0 < β < π 2A) 144145B) 143145Find tan (α + β).C)17145D) 1441786) Find all solutions of the equation.cos x = 1A) x = 3π 2 + 2nπ B) x = π + 2nπ C) x = 0 + 2nπ D) x = π 2 + 2nπ87) Write the expression as the cosine of an angle, knowing that the expression is the right side of the formula forcos (α - β) with particular values for α and β.cos (155°) cos (35°) + sin (155°) sin (35°)A) cos (190°) B) cos (210°) C) cos (120°) D) cos (220°)88) Solve the equation on the interval [0, 2π).(tan x + 1) (cos x + 1) = 0A) 3π 4 , 7π 4 , 2π B) 0, π 4 , 5π 4C) 3π 4 , π, 7π 4D) 0, 3π 4 , 7π 418

89) Find the exact value of the expression.cos ( 2π 9 - π 18 )A)32B) 1 2C) 1 D) 1 490) Identify α and β in the following expression which is the right side of the formula for cos (α - β)cos (170°) cos (50°) + sin (170°) sin (50°)A) α = -170°, β = 50° B) α = - 50°, β = 170° C) α = 170°, β = 50° D) α = 50°, β = 170°91) Complete the identity.sin2 x + tan2 x + cos2 x = ?A) cos3 x B) sin x C) sec2 x D) tan2 x92) Find the exact value of the expression.3sin-12A) π 3B) 2π 3C) π 4D) 3π 493) Find the exact value of the expression.cos-1 -A) 3π 422B) π 4C) -π 4D) -3π494) Find the exact value of the expression.tan-1 (-1)A) - π 4B) π 4C) 5π 4D) 7π 495) Use a right triangle to write the expression as an algebraic expression. Assume that x is positive and in thedomain of the given inverse trigonometric function.cos(sin-1 x)A) 1 - x2 B) x2 + 1 C) x2 - 1 D)x2 + 1x96) Find the exact value of the expression if θ = 45°. Do not use a calculator.(cos θ)2A) 1 2B) 2 C) -22D) 219

97) Find the exact value.sec π 4A)22B) 2 33C) 2 D) 398)a33°b = 12Find the measure of the side of the right triangle whose length is designated by a lowercase letter. Round youranswer to the nearest whole number.A) a = 18 cm B) a = 7 cm C) a = 8 cm D) a = 1 cm99) Use a calculator to find the value of the acute angle θ to the nearest degree.sin θ = 0.8659A) 1° B) 76° C) 60° D) 31°100) Find all solutions of the equation.2 sin x - 3 = 0A) x = π 3 + nπ or x = 2π 3 + nπ B) x = π 6 + 2nπ or x = 5π 3 + 2nπC) x = π 6 + nπ or x = 5π 3 + nπ D) x = π 3 + 2nπ or x = 2π 3 + 2nπ101) Use substitution to determine whether the given x-value is a solution of the equation.cos x + 1 = sin x, x = -7π4A) Yes B) No102) Solve the equation on the interval [0, 2π).cos 2x =22A) 0, 2π 3 , π, 4π 3B) π 8 , 7π 8 , 9π 8 , 15π8C) π 4 , 3π 4 , 5π 4 , 7π 4D) no solution103) Solve the equation on the interval [0, 2π).sin2 x + sin x = 0A) 0, π, 3π 2B) 0, π, 4π 3 , 5π 3C) 0, π, π 3 , 5π 3D) 0, π, π 3 , 2π 3104) Solve the equation on the interval [0, 2π).2 cos2 x + sin x - 2 = 0A) π 2 , 3π 2 , π 3 , 2π 3B) π 6 , 5π 6C) π 3 , 2π 3D) 0, π, π 6 , 5π 620