Mathematical Investigations IV
Name:
Polar Coordinates and Complex Concepts
Out and Around in an Imaginative Way
The Exam
Show enough thinking so that someone can easily reconstruct your answer.
1.

where:
a)
both r and  are positive
7 

 2 3,
 or 2 3, 210
6 


2.

If point P, in rectangular coordinates, is: 3,  3 . Find a set of polar coordinates of P
r is negative and  is positive
b)


 2 3,   2 3,30
6




Express the equation x 2  6 x  y 2  0 in the polar form r = f().
x 2  6 x  y 2  0  x 2  y 2  6 x  0  r 2  6r cos  0 or r  6cos
3.
Express the equation r 2  cos(2 ) in simplified rectangular form.
r 2  cos(2 )  r 2  2cos 2   1  r 4  2r 2 cos 2   r 2

 x2  y 2

2

 
 2x2  x2  y 2  x2  y 2

2
 x2  y 2
Polar & Complex Exam.1
S08
Mathematical Investigations IV
4.
Name:
Write an equation describing the following graphs:
5
a) r  3  3sin( )
5.
b) r  5cos(5 )
Sketch the graph of the limacon r  2  4sin( ), 0    2 .
(Label all intercepts using polar coordinates)

(6, )
2
( 2,
(2,  )
Polar & Complex Exam.2
3
)
2
(2,0)
S08
Mathematical Investigations IV
Name:
6. Sketch the graph of the limacon r  4sin(2 ), 0    2 .
(Label all significant points using polar coordinates)
( 4,
7
)
4
(4,
5
)
4
Polar & Complex Exam.3

(4, )
4
( 4,
3
)
4
S08