# Math Help - Curvature Problem (What Am I Doing Wrong?)

1. ## Curvature Problem (What Am I Doing Wrong?)

Find the curvature "k" of r(t) = <-t+sint , 1+cost>

I'm using the formula: (magnitude of cross product of a and v) / ((magnitude of velocity)^3)
I got:
v(t) = <-1+cost, -sint>
a(t) = <-sint, -cost>
mag. of cross prod. = 1+cost
mag. of velocity = sqrt(2-2cost)
k = (1+cost)/((2-2cost)^(3/2))

This answer is not correct. What am I doing wrong?

2. ## Re: Curvature Problem (What Am I Doing Wrong?)

For curvature use:

$\kappa =\frac{x'(t) y''(t)-x''(t) y'(t)}{\left(x'(t)^2+y'(t)^2\right)^{3/2}}=$

$=-\frac{1}{2 \sqrt{2-2 \text{cos}(t)}}$