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anonymous
 5 years ago
Determine the parametric equations of the tangent line to the curve r(t) =< cos 2t; sin 3t; sin 4t >
when t = pi/4
anonymous
 5 years ago
Determine the parametric equations of the tangent line to the curve r(t) =< cos 2t; sin 3t; sin 4t > when t = pi/4

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0we want the time derivative of r(t) r'(t)=<2sin(2t), 3cos(3t), 4cos(4t)> now find r'(pi/4) r'(pi/4)=<2, 3sqrt(2)/2, 4> so we have a direction vector, now we want a point on the line. We can use r(pi/4) r(pi/4)=<0, sqrt(2)/2, 0> so the equation of the tangent line is T=<2s, sqrt(2)/2(3sqrt(2)/2)*s, 4s> where s is an arbitrary parameter.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I took the derivative but was unsure where to go from there, thanks!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0in the last equation why the variables swapped?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so it's not confused with t, since it doesn't need to be the same variable.
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