Math 142
Summer 1999
Final Exam
1. (18 pt) Consider the following triangle: t
r q
s
State all six of the trigonometric functions in terms of r,s,
and t.
2.
(15
pt) Let 
.
a)
What
is the period of 
b)
What
is the amplitude of 
c)
Sketch
the graph of 
(one period will do).
3.
(12
pt) Assume that you have a triangle with angle 30° and the two following sides
being 3 and 2 (A,S,S).
a)
Find
all possible triangles with this data.
b)
For
each triangle that you find, determine the area.
4.
(18
pt) Solve the following trigonometric equations:
a)
b)
c)
5.
(12
pt) Find the three complex cube roots of –27i.
6.
(20
pt) Consider the points 
and 
a)
Find
the vectors 
and 
.
b)
Find
and 
c)
Find
d)
Find
the angle between the vectors 
and 
7. (15 pt) Graph the polar equation 
(Hint: you need a
longer period since we have 
instead of 
)