Download Math 1316 – Review for Final Exam

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)