MTH 111/CCE

University of Rhode Island

Instructor: Dr. M. Kulenovic

 Exam #3

                                                                       Providence 5/02/98
Please show your work
 

1.   Let q be an angle in standard position whose terminal side contains the point (-1,3). Find sin q , cos q , tan q , and q .

2.  Find the exact value of tan(cos -1 (1/4)).

3.   Let  f(x) = 4 cos(p/2 - x). For this function find its amplitude, period, and phase shift and sketch its graph on the interval [0,4p].

4.   A tower is 100 feet high and from its top the angle of depression of an object on the ground is 42o .
(a)  Determine the distance from the base of the tower to the object.
(b)  How far is the object from the top of the tower ?

5.   In the right triangle a = 7, c = 16. Find b, and angles a  and  b.

6.   Find the exact value of cos (.a + b ), given that sin a = 2/5, and  be an angle in quadrant I and  cos  b =-1/4, and b be an angle in quadrant II.

7.   Find the exact values of  tan (2q), and cos (2q)  given  cos q = 5/13, and  q be an angle in quadrant I.

8.   Find the angle between the lines   y = 2x + 1, and  y = - x - 2.

9.   Find the exact values of  cos (q/2), and sin (q/2)  given that tan q = 4, and  q be an angle in quadrant I.

10. Find all solutions to  cos2 x = 3/4 in the interval  (0,2p).