1. The problem statement, all variables and given/known data Given the polar function r = 4cos(3θ) find the curvature. 2. Relevant equations 3. The attempt at a solution I know there is a formula for curvature of a polar function but I was never given that equation and was told to convert to parametric. and use ||v x a|| / ||v||^3. So this is my work Converting to parametric: x = 4cos(3θ)cos(θ) y= 4cos(3θ)sin(θ) z = 0 to get v i took the derivative x' = -12sin(3θ)cos(θ) - 4cos(3θ)sin(θ) y' = -12sin(3θ)sin(θ) + 4 cos(4θ)cos(θ) z' = 0 I then took the second derivative to get a x'' = -40cos(3θ)cos(θ) + 24sin(3θ)sin(θ) y'' = -40cos(3θ)sin(θ) - 24sin(3θ)cos(θ) z'' = 0 However I feel like i did something wrong because to computer ||v x a|| would be really messy. Is there any way to simplify before I do the cross product or is there is easier way and I'm just doing the problem wrong? Thanks any help is appreciated.