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# Find the curvature k(t)?

Find the curvature k(t) of the curve r(t)=(−2sint)i+(−2sint)j+(−5cost)k

Please help with work!

Thank You.

### 1 Answer

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- kbLv 77 years agoFavorite Answer
Since r(t) = <-2 sin t, -2 sin t, -5 cos t>, we have by differentiation:

r'(t) = <-2 cos t, -2 cos t, 5 sin t>

r''(t) = <2 sin t, 2 sin t, 5 cos t>.

So, r'(t) x r''(t) = <-10, 10, 0>.

Therefore,

k(t) = ||r'(t) x r''(t)|| / ||r'(t)||^3 = 10√2 / (8 cos^2(t) + 25 sin^2(t))^(3/2).

I hope this helps!

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