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I DIRECTIONS: WORK OUT ALL PROBLEMS ON A SEPARATE PIECE OF PAPER. Review all Tests, Quizzes, and Projects from the semester.You are allowed to bring 1 handwritten 3x5 formula notecard to the final exam. The notecard cannot have the unit circle written on it. You will turn this notecard in with your final exam.Unit 1: Angles, Unit Circle, Right Triangle 1. Give the angle measure represented by each rotation. 2.75 rotations clockwise [A] -795° [B] -495° [C] -990° [D] -275° 2. Find the least positive angle measurement that is conterminal with the given angle. -270° [A] 90° [B] 450° [C] 180° [D] 360° 3. Use the unit circle to find the value of tan 270°. [A] 1 [B] 0 [C] -1 [D] undefined 4. Given the Right Triangle RST where T is the 90°. Round to the nearest tenth. If r = 32.6 and s = 7, find S. [A] S=77.9° [B] S=11.8° [C] S=12.1° [D] S=78.2° 5. Change 4.53 radians to degree measure. Round to the nearest tenth. [A] 259.5° [B] 233.6°[C] 815.4° [D] 14.2° 6. Change -105° to radian measure.7. For a circle of radius 8 feet, find the arc length s subtended by a central angle of 18°. 8. In right triangle ABC, A = 28°, b = 7, and <C is the right angle. Solve the triangle. [A] B=62°, a=3.7, c=7.9 [B] B=62°, a=7.9, c=3.7 [C] B = 62°, a=' 6.2, c = 9.4 [D] B=62°, a=33, c=7.7 9. Change 2.37 radians to degree measure. Round to the nearest tenth.10. If sec?=587 find sin ?.[A] sinθ=37[B] sinθ=587 [C] sinθ=35858 [D] sinθ=358 11. Given cos ?=25 and csc?<0, find sin? and tan?.12. In right triangle RST, if s = 33 and r = 39, find angle S if angle T is the right angle. 13. For a circle of radius 8 feet, find the arc length s subtended by a central angle of 24o.[A] s = 165π feet [B] s = 3215π feet[C] s = 1615π feet[D] s = 192π feet14. If cos θ=45, find tan θ.15. Find sin θ if θ is an angle in standard position and the point with coordinates (0, -4) lies on the terminal side of the angle.16. Given right triangle ABC, find the values of the six trigonometric ratios for angle A if a = 12m and c = 15 m. 17. In right triangle ABC, A = 76o, a = 13, and <C is the right angle. Solve the triangle.18. Change 4.88 radians to degree measure. Round to the nearest tenth.19. Change -240o to radian measure in terms of π.20. Given sin X = 511 and sec X < 0, find cos X and tan X.21. In a right triangle ABC, A = 28o, b = 7, and <C is the right angle. Solve the triangle.22. Change 3.73 radians to degree measure. Round to the nearest tenth.23. Given cos θ = 110 and csc θ < 0, find sin θ and tan θ.24. Evaluate sin(Arccos(-985))25. Solve each equation if 0°≤X≤360°. Sin x= 026. Name the four angles whose tangent equals 0.27. In right triangle SRT, if t = 20.6, r = 7.3, and <T is the right angle, find S.Unit 2: Graphing Trig Functions1. Find the Value of tan?(cos-132)2. Find the Value of cot?(sin-153)3. Find the value of sin?(arccos(-229) 4. Find the amplitude, period, and phase shift of fx=-6sin5x-2.5. Write an equation of the form y=asin bx, where a>0 and b>0, with amplitude 23 and a period of 12. 6. Describe the graph y=3cscx-π5+2.7. Find the amplitude, period and phase shift of f (x) = -4 tan (6x – 2). 8. Find the arc length when the radius = 15 ft , and ?= 35°. [a] 35π12 ft [b]525 ft[c]35π24 ft[d]1050 ft9. At the local QuickTrip, the monthly sales S (in gallons) of Diet Coke is modeled by S=120.3+46.1sin2πt30-5.8 where t is the time in months with t=1 corresponding to January.(a) What is the period of the model? Is this what you expected? Explain.(b) What is the average daily fuel consumption? How do you know?(c) What is the maximum consumption? 10. Write the equation of the cotangent function with a period of , an vertical stretch of 3, a phase shift right by and vertical shift up by 2. 11. Write the equation of the cosine function that is reflected across the x-axis with a period of , an amplitude of 1, a phase shift left by and vertical shift down by 3. Fill in the chart.AmplitudePeriodPhase ShiftVertical Shift12. y=cotx-π2-213. y=12csc(2x+π2)14. y=2tanx15. y=sin35x Graph: 16.y=tan2θ-π+1 17.y=cotθ-π2-135916874292left5514318. y=3sin12θ-π+2 19.y=sec4θ35916874292left55143Unit 3: Law of Sine and Law of Cosine1. Given a triangle with a = 7, A = 17°, and B = 32°, what is the length of c? Round to the nearest tenth. [A] 18.1 [B] 1.6 [C] 3.9 [D] 12.72. Given a triangle with a = 11, A = 29°, and B = 20°, what is the length of c? Round to the nearest tenth. [A] 7.8 [B] 15.6[C] 17.1 [D] 6.13. Find the area of the triangle with a = 4 feet, b = 6 feet and c = 7 feet. Round to the nearest tenth. [A] 4.1 ft2[B] 12 ft2[C] 9.6 ft2[D] 13.2 ft24. Find the area of the triangle with a = 8 feet, b = 5 feet and c = 9 feet. Round to the nearest tenth.[A] 19.9 ft2 [B] 15.9 ft2[C] 6 ft2[D] 21.9 ft25. How many triangles are there that satisfy the conditions a = 15, b = 8, a = 62°? [A] 2 [B] 0 [C] 1 [D] impossible to determine6. Given a triangle with b = 7, c = 5, and A = 122° what is the length of a? Round to the nearest tenth.[A] 9.6 [B] 5.9 [C] 6.1[D] 10.57. Given a triangle with b = 6, c = 7, and A = 114° what is the length of a? Round to the nearest tenth. [A] 7.2 [B] 7.1 [C] 10.1 [D] 10.98. How many triangles are there that satisfy the conditions a = 8, b = 9, A = 77o?9. Given a triangle with a = 10, A = 19°, and B = 20°, what is the length of c? Round to the nearest tenth.A. 19.3B. 5.1C. 9.5D. 10.510. Given a triangle with a = 9, A = 25°, and B = 36°, what is the length of c? Round to the nearest tenth.A. 12.5B. 18.6C. 6.5D. 2.411. Find the area of the triangle with a = 4 feet, b = 10 feet and c = 11 feet. Round to the nearest tenth.A. 24 ft.2B. 5.6 ft.2C. 20 ft.2D. 18 ft.212. Find the area of the triangle with a = 3 feet, b = 5 feet, and c = 6 feet. Round to the nearest tenth.A. 9 ft.2 B. 8.2 9 ft.2C. 2.8 ft.2 D. 7.5 ft.213. How many triangles are there that satisfy the conditions a = 15, b = 6, A = 60°?14. Given a triangle with b = 2, c = 7 and A = 102° what is the length of a? Round to the nearest tenth.A. 6.9B. 7.5C. 7.7D. 6.615. Given a triangle with b = 8, c = 10, and A = 38° what is the length of a? Round to the nearest tenth.A. 10B. 6.8C. 17D. 6.216. Find the measure < A, with a = 6 feet, b = 7 feet, and c = 12 feet. Round to the nearest tenth. A. 24.6oB. 14.6oC. 20.8o D. not possible17. How many triangles are there that satisfy the conditions a = 11, b = 7, A = 61o?18. Find the area of the triangle. Round to the nearest tenth. b = 8, c = 7, < A = 83.3oA. 17.7 units2B. 31.5 units2C. 27.8 units2D. 25.1 units2 Unit 4: Solving Trig Functions and Identities1. Verify that cotx=cscxsecx is an identity. 2. Verify that (sinx-cosx)2=1-2sin?xcos x is an identity. 3. Verify that cos2x=sec2x-tan2x-sin2x is an identity. 4. Verify that cot2x+sin2x=csc2x-cos2x is an identity. 5. Verify that cos2x(sec2x-1)=sin2x is an identity. 6. Find cot x if sinxcotxcscx=37. Find Cos if sin2x-1cosx=-18. Solve each equation if 0 ≤ x ≤ 2π . cos θ = -12 A. 3π4, 5π4B. 5π6, 7π6C. 7π6, 11π6D. 2π3, 4π39. Simplify the expression 11-cosx+11+cosx. [a] 2sec2x [b]2csc2x [c]2cscx [d]csc2x 10. Write the expression in factored form as an algebraic expression of a single trigonometric function.sin2x-3sinx+2[a] (sinx+2)(sinx+1) [b](sinx-2)(sinx+1) [c](sinx+2)(sinx-1) [d](sinx-2)(sinx-1) 11. Find all solutions in the interval [0, 2π). 2sin2x=sinx. [a] x= π2, 3π2, π3, 2π3 [b]x=π3, 2π3 [c]x=π6, 5π6 [d]x=0,π, π6, 5π612. Use trigonometric identities to find the exact value of cos 15°. [a] 6+2 [b]-6+24[c]2+64[d]6-2413. If A and B are the measures of two first quadrant angles and sin A= 45 and sin B= 513,Find cos (A+B)Find tan( A-B)14. If sin ?= 3/5 and ? terminates in the first quadrant find the exact value of cos 2?B. Sin 2?C. tan 2?15. Use the Half angle formula to find tan(165). ................
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