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Math 1316 Review for Final Exam Final Exam is Tuesday, May 12, 2015, 9:00 – 11:00 a.m. You will need a calculator with trig functions (NOT a graphing calculator) for this test. I will provide the trig identities and the formulas from chapters 3 and 4 for you to use. You may prepare one page of notes to use on the test (8 ½” x 11”, front & back OK). In addition to this review sheet, you should study old reviews, tests, and homework. 1. For θ = 785o, draw θ in standard position, give two angles which are coterminal with θ and give the reference angle, θ’. 2. Given the right triangle with adjacent side = 15 and hypotenuse = 17, find sin α, cos α, and tan α. 3. If (-3, -4) is a point on the terminal side of angle φ in standard position, draw φ and use the x-y-r definitions to find sin φ and tan φ. 4. Give the exact value of each. Values from calculators will not be accepted. b) sin 180o c) tan( −3π / 4) d) sec 135o e) cot 330o a) csc(7π / 4) f) sin[tan-1 (-12/5)] 5. Describe all of the transformations from the basic graph for each of the given functions: 1 2 π a. y = − sec( x − ) − 3 b. y 4 tan(2 x + = 4 π 3 ) π = y 3 sin( x − ) 6. Graph at least one period of: 4 15 sin A = 17 7. Given: 8. Given: cos A = − 2 5 and A is in QII ; tan B = and A is in QIII. 5 12 and B is in QIII. Find: cos(A – B) Find: cos 2A 9. Verify the identity: cos x cos 2x = cos x – sin 2x sin x 10. Solve the equation. Give all answers in the first revolution. You may give either radians or degrees: 2 sec 2x – 1 = 4 sec 2x + 3 11-12 Answer the requested question regarding each triangle. 11. a = 15; b = 27; c = 38 ; Find B. 12. A = 52O; a = 83, B = 12O ; Find b. 13. An observer in a lighthouse is 66 m above the surface of the water. He sees a ship at an angle of depression of 40O. How far is the ship from the base of the lighthouse? 14 - 16 Let v = 4,7 and w = −1,2 14. Find 2v + 6w 15. Find the direction angle for w. 16. Find the magnitude of v, the magnitude of w, and the dot product of v and w. Use these to calculate the angle between v and w. 17. Plot the complex numbers on a complex plane (Label with letter): b) -2i c) 3 cis 180o d) 2 2 cis 315o a) −1 + i 3 18. Change the complex number from trig form into standard form: 5 cis 210O. 19. Change the complex number from standard form to trig form: 4 3 − 4i . 20. Multiply in trig form, then give answer in standard form: (3 cis 230o).(2 cis 250o) 21. Divide in trig form, then give answer in standard form: (8 cis 120o) / (4 cis 30o) 22. Raise to the power using DeMoivre's Theorem; give answer in standard form: (3 cis 315o)4. 23. Find the three cube roots of 8i . Give answers in standard form. 24. Convert: a) (4, π) from polar into rectangular. b) (3 3, 3) from rectangular into polar. --------------------------------------------------------------------------------------------------------------------------------Answers: 1. 3. coterminal: 425o , 65o, ref angle: 65o sin α = 8/17, cos α = 15/17, tan α = 8/15 sin φ = -4/5, tan φ = 4/3 a) − 2 b) 0 c) 1 d) − 2 e) − 3 f) -12/13 a) vertical reflection; vertical shrink by ½; hor. trans. to right π/4; vertical trans. down 3 b) vertical stretch by 4; new period = π/2; horizontal trans. to left π/6. 6. graph -----> 7. 21/221 8. -17/25 3 9. proof 10. {60o, 120o, 240o, 300o} 11. 34.46o 12. 21.90 π/4 5π/4 7π/4 11π/4 13. 78.66 m 14. <2, 26> -3 o 15. 116.57 16. 65, 5, 10 , 56.31o 17. graph -----> 1. 2. 3. 4. 5. 18. − 19. 20. 21. 22. 23. 5 3 5 − i 2 2 2 8 cis 330o −3 + 3 3i 2i -81 3 + i , − 3 + i , − 2i { 24. a) (-4, 0) (a) 1 -3 -2 -1 (c) } b) (6, π/6) or (-6, 7π/6) 0 -1 -2 (b) 1 2 (d) 3