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

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.