MTH 111 - FALL 2000 - REVIEW PROBLEMS FOR TEST 3
NOTE: The third test will be held on December 04, 2000 (Monday) 6:00 - 7:30 PM. The questions for the test will be from sections 4.2 through 5.5 in the syllabus. The room assignments are as follows:
Sec 1,2,4,6/92,9,12,13 in BISC AUD, Sec 7,8,10,11,14,15 in Chafee 271, Sec 3/93 in Chafee 273, Sec 5/94 Tyler 106.
1. cos q, cot q, csc q for an angle q in standard position whose terminal side contains the point (-5, 6)
2. For the function f (x) = - 3 cos (2x + p/2 ) , find the (a) amplitude (b) period (c) phase shift. Sketch the graph of f .
3. (a) Let q be in quadrant IV. If cos q = 12/13, find the exact value of cot q. b) Find cos (2x) if cos x = 5/13 and x
is in quadrant IV. (c) Find the exact value of sin (a - b) if sin a = 3/5 and cos b = - 2/5, with a in quadrant II and b
in quadrant III.
4. Use identities to simplify : (a) sin (x +p /3) - cos (x +p /6) (b) sin (2x) cos x - sin x cos (2x)
(c) cos x cos (60° + x) + sin x sin (60° + x) (d) sin 2 q + sin 2 q ( csc2 q + cot 2 q)
5. Let cos q = x. Express sin q, tan q, sec q, csc q, cot q in terms of x.
6. Find all the solutions of x in [ 0, 2p]:
(a) csc x = 2 (b) cos2 x = 4 cos x (c) tan 2x = -1 (d) sin 2x + sin x = 0 (e) 5 sin2 x - sin x - 4 = 0
7. Find the exact values of : (a) cos 345° (b) cos 75° (c) tan 15° (d) sin 112.5° °
8. An observer stands on a level ground 200 meters from the from the base of a TV tower. The angle of elevation from
the observer to the top of the tower is 30° . Find the height of the tower above the observer’s eye level?
9. (a) A kite flies at a height of 60 ft when 130 ft of string is out. Assuming that the string is in a straight line what is
the angle that it makes with the ground? (b) Find the height of a tree if the angle of elevation of its top changes from
20° to 40° as the observer walks 75 towards its base.
10. Solve the triangle ABC given that a = 43°, g = 57°, a= 4.56.
11. Solve the triangle ABC given that a = 24, c = 32, and b = 115°
12. Given that a = 40, c = 45 and b = 72 ° Solve the triangle and find its area.
13 If two spokes of a wheel of radius 3 ft. determine an angle of 23° at its center, what is the length of the arc determined
along the rim?
14. A railroad curve is to be laid out on a circle. What radius should be used if the track is to change direction 30° in a
distance of 180 feet?
NOTE: The final exam will be held on Friday, Dec 15, 2000, 8:00 - 11:00 AM in Edwards Aud. The material covered in the three tests and the three Review sheets will provide a good review for final.