- #1

shards5

- 38

- 0

## Homework Statement

Find the curvature K(t) of the curve r(t) = (-4sin(t)) i + (-4sin(t)) j + (5cos(t)) k.

## Homework Equations

K(t) = |r'(t) x r"(t)| / |r'(t)|

^{3}

## The Attempt at a Solution

r'(t) = (-4cos(t))i + (-4cos(t))j + (-5sin(t))k

r"(t) = (4sin(t))i + 4sin(t))j + (-5cos(t))k

|r'(t)| = sqrt(16cos

^{2}(t) + 16cos

^{2}(t) + 25sin

^{2}(t))

r'(t) x r"(t) = [20cos(t)+20sin(t)]i - [20cos(t) + 20sin(t)]k +0j

|r'(t) x r"(t)| = sqrt([20cos(t)+20sin(t)]^2 + [-20cos(t) - 20sin(t)]^2)

Answer should be:

sqrt([20cos(t)+20sin(t)]^2 + [-20cos(t) - 20sin(t)]^2)/[sqrt(16cos

^{2}(t) + 16cos

^{2}(t) + 25sin

^{2}(t))]

^{3}

But it isn't, so I am confused as to what I am doing wrong.