a cardiod microphone pattern is given by the following equation:

the expanded form of this equation is

(a) Find the intercepts of the graph of the equation

to find

I set

thus resulting in

so

to find

I set

thus resulting in

so

are

(b) Test for symmetry with respect to the x-axis

my questions is that i do not how the symmetry is found except by observation from the graph. so symmetry is only on x-axis not on y-axis.

the books answers were

**(a)** **(b)**x=axis symmetry

but wolfframalpha gave something else

btw like the upgrades to latex