Ch. 9 Parametric Equations And Polar Plots

Question 0

What are the equations of a Limacon

Answer 0

+
r = a - b cos theta
+
r = a - b sin theta

Question 1

How do you eliminate the parameter

Answer 1

Solve for t in one equation
Substitute into the second equation
Result is a rectangular equation

Question 2

What are the equations of a cardioid

Answer 2

+
r = a - a cos theta
+
r = a. - a sin theta

Question 3

What are the equations of a rose curve

Answer 3

r = a cos n theta

r = a sin n theta

Question 4

How many petals does a rose curve have if n is an even number

Answer 4

Two times the amount of n

Question 5

How many petals to say Rose curve have if the n of value is odd

Answer 5

N number of petals

Question 6

What is the equation of a Lemniscate

Answer 6

2. 2
   r. = a. sin 2 theta
   2. 2
      r = a. cos 2 theta

Question 7

What is the equation of a circle

Answer 7

r = a cos theta

r = a sin theta

Question 8

How do you find multiple representations of polar points

Answer 8

Keep the point the same and either add or subtract two pie

Or take the opposite of r and then either subtract or add pie

Question 9

What are the Coordinate conversion equations

Answer 9

x = r cos theta
y = r sin theta 
                    x
Tan theta = ---
                    y
  2.      2.     2
r.   = x.  + y

Question 10

What are the quick tests for symmetry in polar coordinates

Answer 10

r = f (sin theta). Symmetric to
theta = pie / 2

r = g (cos theta). WRT polar axis

Question 11

What is the symmetry like for a rose curve

Answer 11

The Rose curves can have more symmetry than their respective functions imply

Question 12

What is the symmetry of a Lemniscate

Answer 12

May be symmetric to the pole as well as the polar axis and the line theta = pie / 2