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College Trigonometry Final Exam Name:___________________________ (1-12 are worth 3pts each, 13-28 are worth 4pts each) Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Write an equation of a parabola with a vertex at the origin and a focus at (0, –2). a. c. b. ____ d. 2. Find the measure of the angle below. y 15 x a. 255º b. 90º c. 105º ____ 3. In which quadrant does the terminal side of a –322º angle lie? a. second quadrant c. third quadrant b. fourth quadrant d. first quadrant ____ 4. Find the exact value of cos 300º and sin 300º. a. c. b. ____ d. 195º d. 5. A particular sound wave can be graphed using the function . Find the amplitude and period of the function. a. c. 2 5 amplitude = , period = 7 amplitude = , period = –7 5 2 b. d. 2 5 amplitude = 7, period = amplitude = –7, period = 5 2 Sketch the angle in standard position. ____ 6. 320º a. c. y y 320 320 x b. d. y x y 320 320 x x Simplify the trigonometric expression. ____ 7. a. b. Solve the equation for 0 ____ c. d. < 2. Write your answer as a multiple of , if possible. 8. a. c. b. d. Write a cosine function for the graph. ____ 9. y 4 2 O 2 –2 –4 a. c. b. d. ____ 10. Use the Law of Sines. Find to the nearest tenth. C 56 61° B 64 a. 91.7 b. 49.9 A c. 130.1 d. 88.3 ____ 11. Use the Law of Cosines. Find to the nearest tenth of a degree. C 2 3 B 4 a. 52.8 b. 46.6 A c. 62.7 d. 29.0 c. d. Find the exact value of the expression. ____ 12. cos 165° a. b. Short Answer 13. Find the foci of the ellipse with the equation . 14. Graph . . Graph the ellipse 15. Identify the focus and the directrix of the graph of . Write the measure in radians. Express the answer in terms of . 16. –290º Write the measure in degrees. 17. – radians 18. Suppose . Find . 19. The line of sight from a small boat to the light at the top of a 40-foot lighthouse built on a cliff 20 feet above the water makes a 27° angle with the water. To the nearest foot, how far is the boat from the cliff? 40 ft 27 Drawing is not to scale. 20 ft Find the length x. Round to the nearest tenth. 20. x 35 41 ° 21. What is the simplified form of sin(x + )? 22. To find the height of a pole, a surveyor moves 140 feet away from the base of the pole and then, with a transit 4 feet tall, measures the angle of elevation to the top of the pole to be 44 . To the nearest foot, what is the height of the pole? . 23. Find the angle of elevation of the sun from the ground to the top of a tree when a tree that is 10 yards tall casts a shadow 14 yards long. Round to the nearest degree. 24. Perform the indicated operation, where u = < 3,-1 > and v = <- 6,7>. a. b. c. d. v•u 2u - 3v ||u|| + ||v|| Find the angle between u and v. (To the nearest degree.) Simplify, write the complex number in a + bi form 25. (2 + 3i) + (-7 + 2i) 26. (6 + 11i)(8 – 2i) Write the complex number in trigonometric form. 27. z =4 + 2i Find the indicated roots. Write your answer in trigonometric form. 28. The three cube roots of 3 + 2i