Chapter 8 Exam Review
1) Find the unknown sides and angles of these triangles:
2) You happen to know the radio tower on the top of a building is 30 feet tall. To find
how far you are from the building, you measure the angle of elevation to the bottom
of the tower to be 20 degrees, and the angle of elevation to the top of the tower to be
23 degrees. How far from the building are you.
3) Convert the polar coordinate
=3
2
,5),(
r
to a Cartesian coordinate
4) Convert the Cartesian coordinate
)7,4(),( −−=yx
to a polar coordinate
5) Rewrite the equation
9
22 =+ yx
as a polar equation
6) Rewrite the equation
2=x
as a polar equation
7) Rewrite the equation
)sin(2
=r
as a Cartesian equation
8) Rewrite the equation
)2sin(
=r
as a Cartesian equation (hint: use an identity)
9) Sketch a graph of
)3sin(
=r
. For what values of θ is the graph at the origin? The
furthest from the origin?
10) Multiply:
(3 4 )(2 )ii+−
11) Divide:
32
4
i
i
−
+
12) Rewrite in polar form:
5 12i+
13) Rewrite in Cartesian form:
6
7i
e
14) Calculate
45 12i+
. Give your answer in a+bi form.
15) Given the vectors shown, sketch
34uv−
16) A man walks 5 miles north, 3 miles at 30o north of east, 4
miles southeast, and 2 miles west.
a. Draw a picture showing the man’s path as set of
vectors
b. Resolve each vector into components
c. Find the vector showing the man’s total displacement (the vector from where
he started to where he ended up)
d. How far is the man from where he started at the end of his walk?
e. In what direction should he walk to get back to his starting position?
130o
3
5
20o
12
6
