Worked Examples - Parametric Equations
Problem: Find a Cartesian equation from the following set of parametric
equations:
= 2 +
= 2 1
Solution:
Solve for t with one of the equations
= 2 1
2 = + 1
1
= ( + 1)
2
Substitute into the other equation and

Worked Example Finding Area and Arc Length in Polar
Problem: Find the area of the inner loop of = 2 + 4 cos
Solution:
Graph and determine
limits of integration
0 = 2 + 4 cos
1
cos =
2
1
= cos 1 ( )
2
2 4
=
,
3 3
4
3 1
2
3
4
3 1
2
3
2
2
2
(2 + 4 cos )

Worked Examples Tangent Lines and Graphing Polar
Equations
Problem: Find the slope of the tangent line for the polar equation 1 + cos at = 2 .
Solution:
= 2
=
2
Find polar coordinates at the given point
= 1 + cos ( )
2
= 1 + 0
(1, )
2
= 1 + cos ( ) =

Worked Example Polar Coordinates
Problem: Convert from
Solution:
Answer:
to Cartesian coordinates.
Problem: Convert
into polar coordinates.
Solution:
Find r.
Find .
is in first quadrant, the point
Answer:
is in the third quadrant.
Problem: Convert
Solut