Math 142
Summer 1999
Exam 5
1.
(40
pt) For the following parametric equations, find the corresponding Cartesian
equations and sketch the graph (use arrows to indicate the direction).
a) 
b)
c)
, 
d)
, 
2.
(24
pt) A center fielder attempts to throw the ball 400 feet to home plate. Assume
that he throws from a height of 6 feet.
a)
If
he throws flat (
), how fast does he have to throw it to get it to home plate
on the fly (in miles per hour…there
are 5280 feet in a mile)?
b)
What
if he throws it at an angle of 30º (how fast does he have to throw it to get it
to home plate on the fly in miles per
hour)?
3.
(12
pt) Convert the following points:
a)
from polar to Cartesian.
b)
(-20,-21)
from Cartesian to polar.
4.
(18
pt) Find the Cartesian equations from the given polar equations:
a)
b)
c)
(Hint: 
).
5.
(16
pt) Sketch the graph of the polar equation 
. (Show where you get your info…copying from your graphing
calculator is not good enough).