Answer:
The graph is symmetric about the x-axis only
Step-by-step explanation:
* Lets study the limacon curve
- Equations of the form:
# r = a + b sin θ
# r = a – b sin θ
# r = a + b cos θ
# r = a – b cos θ
All will produce limacons.
* Lets examine what happens for various values of a and b.
- When the value of a is less than the value of b, the graph is
a limacon with and inner loop.
- When the value of a is greater than the value of b, the graph is
a dimpled limacon.
- When the value of a is greater than or equal to the value of 2b,
the graph is a convex limacon.
- When the value of a equals the value of b, the graph is a special
case of the limacon. It is called a cardioid.
* Notice that, in each of the graphs of the liamcons, changing
from sine to cosine does not affect the shape of the graph just its
orientation.
- Equations using sine will be symmetric to the vertical axis
- Equations using cosine are symmetric to the horizontal axis.
∵ r = -2 + 3 cos Ф
- from the notes up the equation of cosine is symmetric to
the horizontal axis
∴ The graph is symmetric about the x-axis only
