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Name:_______________________Date:_______________ Trigonometry Final Exam Review Sheet . All work must be shown. Just having answers is not sufficient to receive full credit on the review. 1. Solve the equation if possible: 3x – 2(x + 5) = 10 2. Solve the equation if possible: x² – 12 x + 30 = 0 3. Solve the equation if possible: 12t³ – 84t² + 120t = 0 4. Find the distance between the following two points: (-1, 4) and (2, 0) 5. Find the midpoint between the following two points (-2, 2) and (3, -10) 6. Determine the center and the radius of the following circle: x² + y² – 20x – 10y + 100 = 0 7. Sketch the graph of y = 8 – x 8. Determine the domain of f(x) = x + 2 9. Find the inverse of the function f(x) = x³ + 2 10. Convert 5 to degrees. Be sure to round your answer to two decimal places. 7 11. Convert 8415’ to radians. Be sure to round your answer to 4 decimal places. 12. Find the reference angle of 640 13. Evaluate the trigonometric function without the aid of a calculator: sin (5) 3 14. Find the value of csc 270 15. Given that the cos 29 = .8746, evaluate the cos 151 16. Find the secant of 11 without the aid of a calculator 4 17. Change 320 to radians in terms of 18. Change to degrees 9 19. Write an algebraic expression for sec [arcsin (x – 1)] 20. Find the five remaining functions given that sin = 21. Find the period, amplitude, and five key points of y = 3 cos ( x + ). Then sketch the graph. 22. Sketch y = sin x + 2 11 and cos < 0 61 23. Sketch y = 2 tan x 24. Sketch y = 3csc (x – ) 2 25. Sketch y = –2sec x 26. Sketch y = cot (x – ) 4 27. Sketch y = log3 x 28. Evaluate arccos .28 29. Evaluate arctan (-1) 30. Find the exact value of cos(arctan 2) without the aid of a calculator. 31. Verify the identity. 32. Solve 3tan² x – 1 = 0 on the interval [0, 2) 33. Solve cot x cos² x = 2 cot x on the interval [0, 2) 34. Evaluate ln e³ 35. Evaluate log27 9 csc x – sin x = cos x cot x 36. A 20 foot ladder leaning against the side of a house makes a 75 with the ground. How far up the side of the house does the ladder reach? 37. From a 150-foot observation tower on the coast, a Coast Guard officer sights a boat in difficulty. The angel of depression of the boat is 4. How far is the boat from the shoreline? 38. An amateur radio operator erects a 75-foot vertical tower for his antenna. Find the angle of elevation to the top of the tower at a point on level ground 50 feet from the base. 39. Find the remaining sides and angles of the triangle if A = 24.3, C = 54.6, and c = 2.68 40. Find the remaining sides and angles of the triangle if a = 9, b = 12, c = 15 41. Use Heron’s formula to find the area of a triangle with sides of a = 5, b = 7, c = 10 42. Find the trigonometric form of -4 + 4i 43. 2 Find the standard form of 2(cos2 + i sin ) 3 3 44. Use DeMoivre’s Theorem to find [5(cos 20 + i sin 20)]³ Review Sheet Answers 1. 20 2. 6 ± 6 3. 0, 2, 5 4. 5 5. (.5 , -4) 6. center ( 10, 5) radius = 5 7. see graph 8. x -2 9. f-1(x) = ³ x –2 10. 128.57˚ 11. 1.4704 12. 80 13. 3 2 14. -1 15. -.8746 16. - 2 17. 16 9 18. 20 19. - x² + 2x -x² + 2x 20. cos = - 60 / 61 tan = -11/60 csc = 61/11 sec = - 61/60 cot = - 60/11 21. amp. = 3 per. = 2 key points: (-, 3) ( -/2 , 0) ( 0, -3 ) (/2, 0) (, 3) 22. See graph 23. See graph 24. See graph 25. See graph 26. See graph 27. See graph 28. 1.29 radians or 73.7 29. –/4 30. 5/5 31. answers may vary 32. /6 and 5/6 and 7/6 and 11/6 33. /2 and 3/2 34. 2/3 35. 19.32 feet 36. 2145 feet 37. 56.3 38. B = 101.1, a 1.35 , b 3.23 39. A36.9, B 53.1 , C 90 40. 16.25 sq. units 41. 42 cis 135 42. –1 + i3 43. 125 + 125i3 2 2