NAME: Very Brief Answers
TEST04/MAC1114
Page 1 of 4
Read Me First:
Show all essential work neatly. Use correct
notation when presenting your computations. Write using complete
sentences. In particular, be very careful when using "=",
equals
, and "
⇒
",
implies
.
Do not "box" your answers.
Communicate.
1. (15 pts.)
Identify each of the following polar equations as
completely as possible by transforming each equation to
rectangular coordinates. [These are fairly easy!!]
(a)
θ
= (1/6)
π
This is the straight line through the origin defined by the
equation y = tan(
π
/6) x = 3
1/2
x.
(b) 2r sin(
θ
) = 3r cos(
θ
)
This is the straight line through the origin defined by the
equation 2y = 3x.
(c) r = 3
This is the circle centered at the origin with radius equal
to 3. Its rectangular equation is x
2
+ y
2
= 9.
(d) r = 2 sin(
θ
)
This is the circle with the following rectangular equation:
x
2
+ (y  1)
2
= 1. Consequently, its center is at (0,1) and it
has a radius equal to 1.
(e) r cos(
θ
) = 4
This is simply the line parallel to the xaxis defined by
x = 4.
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 Spring '08
 Storfer
 Cartesian Coordinate System, 5 pts, Polar coordinate system, 15 pts, 10°, prestidigitation

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