Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = 2 cos 5θ?

r = 2 cos(5T)

polar axis or x-axis:

replace T by -T

r = 2 cos(-5T)

Since cos is an even function, cos(-5T)=cos(5T)

equation unaltered.

Equation is Symmetric about the x-axis

———————————-

About y-axis: or the line T = pi/2

replace T by pi – T

r = 2 cos(5T)

r = 2 cos(5(pi-T))

cos(5pi-5T) = cos(5pi)cos(5T) + sin(5pi)sin(5T)

= -cos(5T)

r = -2 cos(5T)

Equation not the same

Not symmetric with respect to y-axis:

————- —————————

origin:

replace r with -r

r = 2 cos(5T)

-r = 2 cos(5T)

r = -2 cos(5T)

Equation not the same

Not symmetric with respect to origin.