the equation for symmetry with respect to the specified axis

the equation for symmetry with respect to the specified axis, line, or pole. r = 4 + 2 sin theta; the line theta = pi/2 May or may not be symmetric with respect to the line theta = pi/2 Symmetric with respect to the line theta = pi/2 r = -4 cos theta; the polar axis May or may not be symmetric with respect to the polar axis Symmetric with respect to the polar axis

Solution

12. r= 4+2sin theta

TO check whether it is symmetric with line theta=pi/2 , we have to plug theta=- theta and r=-r

-r = 4+2sin(-theta)

-r= 4-2sin theta

r= -4 + 2sin theta

And this equation is not equivalent to the original equation

Hence it is not symmetric to the line theta= pi/2

13. r=-4 cos theta

To check whether it is symmetric to pole or not,we have to plug -r for r

-r= -4 cos theta

r=4 cos theta

And this equation is not equivalent to the original equation. Therefore it is not symmetric to pole