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.


If point P, in rectangular coordinates, is: 3,  3 . Find a set of polar coordinates of P
where:
a)
both r and  are positive
b)
r is negative and  is positive
2.
Express the equation x 2  6 x  y 2  0 in the polar form r = f().
3.
Express the equation r 2  cos(2 ) in simplified rectangular form.
Polar & Complex Exam.1
S08
Mathematical Investigations IV
4.
Name:
Write an equation describing the following graphs:
5
a) _____________________
5.
b) ___________________
Sketch the graph of the limacon r  2  4sin( ), 0    2 .
(Label all intercepts using polar coordinates)
Polar & Complex Exam.2
S08
Mathematical Investigations IV
Name:
6. Sketch the graph of r  4sin(2 ), 0    2 .
(Label all significant points using polar coordinates)
Polar & Complex Exam.3
S08