Question

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.

Answer 1

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