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state the symetry

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
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1 Answer

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