state the symetry

Question

I am learning about Graph of polar equation but i dont have a book

 

State the symetry of r=16 cos(2theta)

  

Can someone give my an example so i can lern how to find the symetry of this problem?

 

 

 

Thank you so much

Answer 1

r=16cos(2θ)

 

Symmetry test:

 

If (r,-θ), then r=16 cos 2(-θ)= 16 cos 2θ...... (as cos is an even fun).

x-symmetry----yes

 

If (-r,-θ) ⇒  -r=16 cos 2(-θ) =16 cos 2θ

                  r= -16 cos 2θ

y-symmetry....no

 

If (-r,θ)  ⇒ -r= 16 cos 2θ 

                

 

            r = -16 cos 2θ 

 

symmetry with respect to origin .....no

 

Draw graph ,check answer that it satisfies.

Sometimes it is best to look at the graph of the polar function instead of trusting algebraic manipulation.

 

Meena from Strongsville , OH