Math 142
Summer 2000
Exam 3
(20 pt) Consider the
following piece of a function pictured:
a)
If
the function crosses the 
at the points 0, 2 and 6 and is of period 6. Find a formula
for all the roots of the function.
b)
Assume that the function is odd and of period 12.
Find a formula for all the roots of the function.
6
- (18 pt) Simplify or
evaluate the following:
a) 
b) 
c) 
- (24 pt) Solve the
trigonometric equations (find all solutions):
a) 
b) 
c) 
- (12 pt) Verify the
identity
(you may assume
that denominators are nonzero and 
are defined).
- (15 pt) Two lines pass
through the point (1,1). The first line goes through the point
and the second goes through 
Find the larger
of the two angles formed by the intersection of these two lines.
- (21 pt) While hovering
in a helicopter you notice that two jets pass you at the same time. One
jet is 2 miles above your position and the other is 1 mile below. Both
jets fly at a constant speed of 500 miles per hour.
a)
Find
the angle that you perceive between the two jets as a function of time.
b)
Find
as a function of
time.
q