Question

For the polar equation r=9cos(2theta),
a.) identify the type of curve.
b.) convert the equation to rectangular form. ( use trig Identities)
c.) fint any symmetries

Answer 1

A The polar curves\[r = a \cos (n \theta), r = a \sin (n \theta)\]petalled flowers called roses. If n is even, there are 2n petals, if n is odd, there are n petals.
B. The following substitutions may help:\[\cos (2 \theta) = \cos^2 \theta - \sin^2 \theta, x^2 + y^2 = r^2\]\[r \cos \theta = x, \cos \theta = \frac {x}{r}, rsin \theta = y, \sin \theta = \frac {y}{r}\]C. You can graph the equation to see where the symmetries are.