Download Final Exam Review

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)