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Spring 2011 Math 1316 – Review for Final Exam 1. Suppose that cos θ = – 3/4 (θ in QII). Find the other 5 trigonometric functions of θ. 2. An 11-inch windshield wiper sweeps out an angle of 120º. How far does the tip of the windshield wiper move? 3. A bug is sitting on the edge of a spinning CD. If the bug moves a total distance of 60 inches in 2 minutes, then calculate the linear velocity of the bug in inches per minute. 4. Find the linear speed of a point traveling along the circumference of a circle with a radius of 8 inches and an angular velocity of 516 radians per second. 5. A lighthouse rotates its light in a circular motion with constant speed. If the beacon of light completes one rotation every 8 seconds, what is the angular speed of the beacon in radians per second? 6. Calculate the exact values of: 7. a) Convert 345º to radians. a) sin 120º b) tan π/4 c) 4sin60ºsec315º b) Convert π/12 to degrees. 8. Graph and state the amplitude, period, phase shift and label 5 points along the x-axis. a) y = 3 sin(½ x + π) (graph one cycle) b) y = –4 cos(2x – π) (graph one cycle) 9. Find cos(A + B) if sinA = 4/5 (A in QI), and sinB = – 2/5 (B in QIII). 10. Find sin (A/2) if cosA = 3/5 and A is in QIV. Spring 2011 11. Prove: a) 1 1 1 2 sin x tan 2 x 12. Solve (0 ≤ x < 2π): b) csc x sin x cot x cos x a) tan 2 x 3 tan x 0 b) cos 2 x 2sin x 2 0 13. Eliminate the parameter and write the equation in rectangular form: x 2cos t y 3sint 14. If B = 16.3˚, a = 76.3 in, c = 42.8 in, then find all missing sides and angles (use Law of Sines and/or Cosines when appropriate). 15. Let U = 5i + 6j, V = i – 2j. 16. Find U+V, U–V, |U|, U•V, and the angle between U&V. a) Find the area of the triangle with sides of 5, 6, and 9 inches. b) Find the area of the triangle with sides of a = 7 cm, c = 6 cm, and B = 15° . 17. Let z1 = –10 – 7i, and z2 = 4 + 9i. Write z1 and z2 in trig form. 18. Let z1 = –3 cis135˚ and z2 = 5 cis15˚ . Find z1 • z2 and z1 ÷ z2. 19. Write 3 cis 60˚ in standard form. 20. Find (2 – 2i)5 using DeMoivre’s Theorem (write the number in trig form first and give answer in trig form) 21. Find the three cube roots of: 1 3 i (write the number in trig form first and give all answers in trig form) 22. How long should an escalator be if it is to make an angle of 33° with the floor and carry people a vertical distance of 21 feet between floors? 23. Study vector word problems (Section 7.4)