What type of symmetry does the following polar equation have? r = 2cos(4Θ)

Question

a.

About the origin

b.

All of these

c.

About the x-axis

d.

About the y-axis

Answer 1

look at

r=2cos(4θ)

r=2cos⁴θ-8cos²θsin²θ+2sin⁴θ

√(x²+y²)=(2x⁴-8x²y²+y⁴)/(x²+y²)²,,,,converting to rectangular coordinates.

symmetric to y-axis if expression same for x and -x ,,,check

symmetric to x-axis if expression same for y and -y ,,, check

symmetric to origin if expression is satisfied for (x,y) then expression satisfied for (-x,-y) ,,,check