I have been trying to figure out if this problem could be simplified more.

$\displaystyle sqrt(cos^2(t) cos(2 sin(t))-sin^2(t))$

Thanks

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- Oct 11th 2010, 08:40 AMalexgoSimplification
I have been trying to figure out if this problem could be simplified more.

$\displaystyle sqrt(cos^2(t) cos(2 sin(t))-sin^2(t))$

Thanks - Oct 11th 2010, 08:54 AMJhevon
- Oct 11th 2010, 08:55 AMalexgo
- Oct 11th 2010, 08:58 AMJhevon
- Oct 11th 2010, 09:04 AMalexgo
- Oct 11th 2010, 09:11 AMJhevon
oh! you mean the unit tangent vector? i suppose you were trying to simplify |r'(t)|

in that case, you're way off. your |r'(t)| is incorrect. for the correct one, it is 1.

Hint: you made a sign error. there is a minus (at least one) that should be a plus in what you did. - Oct 11th 2010, 09:34 AMalexgo
AHHH, so when I square I take the negative with it, right?

for $\displaystyle r'(t)=cost \cdot cos(sint) i - cost \cdot sin(sint) j- sint k$

for $\displaystyle |r'(t)|=\sqrt{(cost \cdot cos(sint))^2 +(-cost \cdot sin(sint))^2 +(-sint)^2}$

$\displaystyle |r'(t)|=\sqrt{cos^2t \cdot (cos^2(sint) + sin^2(sint)) +sin^2t}$

$\displaystyle |r'(t)|=\sqrt{cos^2t \cdot (1) +sin^2t}$

$\displaystyle |r'(t)|=1$ - Oct 11th 2010, 10:08 AMJhevon