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MTH 112 Final Exam Review Name_____________________________ 1. If sec θ = - in quadrant III, find the exact value of the cot θ. 2. Use the unit circle to find both exact values between 0 and 2 for 3. Use a sketch of a right triangle to find the exact value for ( ( √ ) in radians. ). 4. Find a sine and cosine equation for the graph. Recall that if y = asin b(x + c) + d; a = amplitude, = period, c = phase shift, and d = vertical shift. 5. Simplify the expression: cos 2 x tan x cot x sin x cos x tan x 6. Verify the identity: 24 7. tan A = in the 3rd quadrant and sin B = 7 8 th in the 4 quadrant, find the exact value: Cos (A + B) 17 8. Solve algebraically for all answers between 0 & 2π: 8cos Ѳ - 7 = 0 9. Solve algebraically for all answers between 0 & 2π: 2sin Ѳ tan Ѳ = 8sin Ѳ 10. Solve the triangle: (round angles and lengths to the nearest tenth) a = 18, B = 21o, c = 30 11. Consider force vectors u & v acting on the same point. Find the resultant magnitude and angle Ѳ. ‖ ‖ = 620 pounds, Ѳ = 146o ‖ ‖ = 840 pounds, Ѳ = 278o 12. Change the rectangular coordinate to a polar coordinate (round to the tenth place) (-8,-2) … where 0 < Ѳ < 360o 13. Change the polar coordinate to a rectangular coordinate (round to the tenth place) 14. Consider vectors: v = -3i - 8j, w = 7i + 2j a. Find the angle between vectors v & w b. Find the resulting vector (r) from v, w; in terms of i & j c. Find the magnitude and direction for r 15. Find a rectangular equation from the parametric equation: x = 2t2 – 4t + 5 y = t - 3 (4,152o)