Polar Coordinates Ï = x 2 + y 2 , θ = arctan (y/n) give where Ï' = dÏ/dθ. Derive this. Use it to find

Polar Coordinates ρ = ˆšx²+ y², θ = arctan (y/n) give

where ρ' = dρ/dθ. Derive this. Use it to find the total length of cardioid ρ = α(1 - cos θ). Sketch this curve.

p + p d0, 12