Precalculus CP Final Exam Review. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
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1 Precalculus CP Final Eam Review Name Date: / / MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Convert the angle in degrees to radians. Epress answer as a multiple of π. 1) 6 π radians π6 radians C) π radians π7 radians 1) ) π radians - π radians C) - π radians - π radians ) ) 1 1 π radians π radians C) π radians π radians ) ) π radians - 8π 9 radians C) - 10π 11 radians - 9π 10 radians ) Convert the angle in radians to degrees. ) 11 π C) 9 6π ) 6) - π 6) - π -90π C) ) π 7) 900π 8 C) 0 Draw the angle in standard position. 8) - π 8) 9) 7π 9) 10) 1π 6 10) 1
2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find a positive angle less than 60 or π that is coterminal with the given angle. 11) C) 7 11) 1) 16π 1) 6π 11π C) - 16π π 1) C) ) Use the Pthagorean Theorem to find the length of the missing side.then find the indicated trigonometric function of the given angle. Give an eact answer with a rational denominator. 1) Find sin θ. 1) C) ) Find csc θ. 1) 1 1 C) ) Find cos θ. 16) C)
3 17) Find tan θ. 9 17) C) 9 9 Find a cofunction with the same value as the given epression. 18) sin 8 cos 8 cot 7 C) cos 7 tan 7 18) 19) cos 69 sin 1 sec 69 C) sin 69 csc 1 19) 0) tan cot 11 cot C) cot 68 sec 0) 1) csc sec sec 11 C) sin sec 66 1) A point on the terminal side of angle θ is given. Find the eact value of each of the si trigonometric functions of θ, or state that the function is undefined. ) (, -) ) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Let θ be an angle in standard position. Name the quadrant in which the angle θlies. ) csc θ > 0, sec θ > 0 quadrant I quadrant IV C) quadrant II quadrant III ) Find the eact value of the each of the remaining trigonometric functions of θ. ) cot θ = - 9, cos θ < 0 ) ) sin θ = -, tan θ > 0 ) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine the amplitude or period as requested. 6) Period of = cos 1 6) π C) π π
4 7) Period of = sin 6π 7) π 1 C) 6π Determine the phase shift of the function. 8) = 1 sin ( + π) 8) π units to the left π C) - π units to the left π units to the left units to the right 9) = sin - π 9) units up π C) units down π units to the left units to the right Graph the function. 0) = sin 0) - MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) = sin + π 1) -
5 - - C) - - Determine the amplitude or period as requested. ) Period of = cos - 8π 7 ) 7 C) π 16π 7 Determine the phase shift of the function. ) = cos + π ) units up π units to the left C) units down π units to the right
6 Graph the function. ) = - 1 cos π ) C) - - 6
7 Use a vertical shift to graph the function. ) = sin 1 - ) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 6) = cos - π + 6)
8 C) Determine the phase shift of the function. 7) = cos (π - ) units to the left units to the left 7) C) units to the right units to the right π Complete the identit. 8) (sin + cos ) 1 + sin cos =? 8) sin C) - sec 0 9) sin + sin cot =? cot C) sin + 1 cot - 1 9) 0) cos + sin cos - sin - cos sin =? 1 - sec csc sec csc C) + sec csc - sec csc 0) 1) Simplif the given epression: (sec + 1)(sec - 1) =? 1) tan ) tan + cos + sin =? ) ) 1 - cos 1 + sin =? ) 8
9 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. ) 1 - cos =? sin -csc - cot csc - cot C) csc + cot csc - cot + 1 ) ) sec csc =? sec + csc sec - csc C) csc - sec sec + csc ) Verif the identit. 6) cscu - cos u sec u= cot u 6) 7) (1 + tanu)(1 - sinu) = 1 7) 8) csc u - sin u = cos u cot u 8) 9) 1 + sec sin = sec 9) 0) cot + csc = csc - 1 0) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the eact value of the epression. 1) cos (17 ) cos ( ) + sin (17 ) sin ( ) - - C) - 1-1) 9
10 Complete the identit. ) cos - π 6 =? ) - C) (cos + sin ) 1 (- cos + sin ) (cos - sin ) - (cos - sin ) Use the given information to find the eact value of the epression. ) sin α =, α lies in quadrant II, and cos β =, β lies in quadrant I Find cos (α - β). ) C) Find the eact value b using a sum or difference identit. ) sin (1-9 ) C) - 1 ) ) sin 16 - ( - 1) ( - 1) C) - ( + 1) ( + 1) ) Find the eact value of the epression. 6) cos cos - sin sin 1 C) 1 6) 7) cos π 9 sin π 18 - cos π 18 sin π 9 7) 1 C) 1 1 Use the given information to find the eact value of the epression. 8) sin α =, α lies in quadrant I, and cos β = 8, β lies in quadrant I Find cos (α + β) C) ) 9) sin α = 1 1, α lies in quadrant II, and cos β =, β lies in quadrant I Find sin (α - β) C) ) 10
11 60) tan α = 0, α lies in quadrant III, and cos β = -, β lies in quadrant II Find sin (α + β) C) ) 61) sin α = 7, α lies in quadrant II, and cos β =, β lies in quadrant I Find cos (α - β). 61) C) Find the eact value b using a difference identit. 6) tan C) ) Use trigonometric identities to find the eact value. tan 0 + tan 110 6) 1 - tan 0 tan C) ) Find the eact value under the given conditions. 6) tan α = 1 8, π < α < π 1 ; cos β = - 9, π < β < π Find tan (α + β). C) ) 6) cos α = - 7, π < α < π; sin β = - 1, π < β < π Find tan (α + β). 6) C) Use the figure to find the eact value of the trigonometric function. 66) Find sin θ. 66) C)
12 67) Find tan θ. 67) C) Use the given information to find the eact value of the epression. 68) sin θ =, θ lies in quadrant I Find cos θ. 68) C) 7 69) cos θ = 1, θ lies in quadrant IV Find sin θ. 9 69) C) ) tan θ = 1, θ lies in quadrant III Find sin θ. 8 70) C) Write the epression as the sine, cosine, or tangent of a double angle. Then find the eact value of the epression. 71) cos 1 - sin 1 71) - 1 C) 1-7) tan π tan π 8 7) 1 C) -1 Use a half-angle formula to find the eact value of the epression. 7) sin 16 7) C)
13 7) cos π 1 7) C) Use the given information to find the eact value of the trigonometric function. 7) sin θ = 1, tan θ > 0 Find cos θ. 7) C) ) cos θ = -, sin θ > 0 Find cos θ. 76) 0 10 C) ) csc θ = -, tan θ > 0 Find cos θ. 77) C) Find all solutions of the equation. 78) sin - = 0 78) = π + nπ or = π + nπ = π 6 + nπ or = π + nπ C) = π 6 + nπ or = π + nπ = π + nπ or = π + nπ 79) tan sec = - tan 79) = π + nπ or = π + nπ or = nπ = π + nπ or = π + nπ or = nπ C) = π + nπ or = π + nπ or = nπ = π + nπ or = π + nπ or = nπ Solve the equation on the interval [0, π). 80) sin = 80) 0 0, π, π C) π, π π 1, π 6, π, 7π 1, 7π 6, 1π 1, π, 19π 1 81) cos + cos + 1 = 0 81) π π, 7π C) π π, π 1
14 8) sin = sin 8) π 6, π 6 π, π C) 0, π, π 6, π 6 π, π, π, π 8) cos = sin 8) π, 7π π, π C) π, 7π π, π Solve the equation on the interval [0, π). 8) cot cos = cot 0, π π, π C) 0, π π, π 8) Solve the equation on the interval [0, π). 8) sec - = tan 8) π 6 no solution C) π π 86) cos = 86) 0, π, π, π C) π 8, 7π 8, 9π 8, 1π 8 π, π, π, 7π no solution 87) sin = 1 87) 0, π, π, π π, π, π, 7π C) π 8, 9π 8 no solution 88) cos = - cos 88) 0, π, π, π C) π 8, 7π 8, 9π 8, 1π 8 π, π, π, 7π no solution 89) sin + sin = 0 89) π 8, 9π 8 0, π, π, π C) π, π, π, 7π no solution Use a calculator to solve the equation on the interval [0, π). Round the answer to two decimal places. 90) cos = ,.1 0.7,. C) 0.7, ,.0 90) 1
15 91) sin = ,. 0.9,.99 C) 0.9, ,.8 91) Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. 9) B = 6 C = 107 b = 1 A =, a = 1., c = 19.6 A = 7, a = 19.6, c = 1. C) A =, a =., c = 1.6 A = 7, a = 1.6, c =. 9) Two sides and an angle (SS of a triangle are given. Determine whether the given measurements produce one triangle, two triangles, or no triangle at all. Solve each triangle that results. Round lengths to the nearest tenth and angle measures to the nearest degree. 9) A = 0, a = 7, b = 1 9) B = 60, C = 60, c = 1.1 no triangle C) B = 90, C = 60, c = 1.1 B = 60, C = 90, c = 1.1 9) B =, b = 18, a = A = 1, C = 11, c = A =, C = 116, c =. C) no triangle A = 9, C = 117, c = 0 9) 9) B = 8, b =.9, a =. A1 = 0, C1 = 1, c1 = 8.9; A = 10, C =, c = 0. A = 10, C =, c = 0. C) A = 0, C = 1, c = 8.9 no triangle 9) Find the area of the triangle having the given measurements. Round to the nearest square unit. 96) B = 1, a = feet, c = 9 feet 17 square feet square feet C) 9 square feet 19 square feet 96) Solve the problem. 97) A surveor standing 9 meters from the base of a building measures the angle to the top of the building and finds it to be. The surveor then measures the angle to the top of the radio tower on the building and finds that it is 6. How tall is the radio tower? 11.7 meters meters C) 7. meters 8.6 meters 97) Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. 98) a = 7, b = 1, c = 1 A = 8, B = 70, C = 8 A = 6, B = 70, C = 8 C) A = 0, B = 68, C = 8 no triangle 98) 99) b = 6, c = 10, A = 107 a = 18.9, B =, C = 9 a = 1.1, B = 6, C = 7 C) a = 16, B = 8, C = no triangle 99) 1
16 Solve the problem. 100) Two airplanes leave an airport at the same time, one going northwest (bearing 1 ) at mph and the other going east at 7 mph. How far apart are the planes after hours (to the nearest mile)? 70 miles 108 miles C) 117 miles 16 miles 100) 16
17 Answer Ke Testname: PRECALCULUS CP FINAL EXAM REVIEW 01 1) A ) C ) B ) D ) C 6) D 7) D 8) 9) 10) 11) D 1) A 1) B 1) D 1) B 16) B 17) C 18) C 19) A 0) C 1) D ) ) A 17
18 Answer Ke Testname: PRECALCULUS CP FINAL EXAM REVIEW 01 ) 97 ) - 6) B 7) B 8) B 9) D 0) - 1) C ) A ) B ) A ) ) A 7) D 8) A 9) B 0) B 1) 1 ) sec ) sin ) B ) D -6 18
19 Answer Ke Testname: PRECALCULUS CP FINAL EXAM REVIEW 01 6) cscu - cos u sec u = cscu - cos u 7) (1 + tanu)(1 - sinu) = secu cosu = 8) csc u - sin u = 1 cos u = csc u - 1 = cotu 1 cosu cos u = 1 1 sin u - sin u = 1 - sin u = cos u cos u = cos u = cos u cot u sin u sin u sin u 9) 1 + sec sin = 1 + sin cos = 1 + tan = sec. 0) cot + csc = csc csc = csc ) C ) B ) C ) D ) B 6) A 7) D 8) C 9) C 60) A 61) C 6) C 6) B 6) C 6) D 66) A 67) A 68) B 69) A 70) B 71) A 7) B 7) C 7) D 7) D 76) B 77) A 78) D 79) C 80) D 81) A 8) C 8) B 8) B 8) B 86) C 87) B 88) C 89) B 19
20 Answer Ke Testname: PRECALCULUS CP FINAL EXAM REVIEW 01 90) B 91) D 9) B 9) C 9) C 9) A 96) B 97) B 98) A 99) B 100) B 0
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