Arc length of r(t) = (cost-2)*i + sin2t*j + 2*k from 0 to pi?
Hello,
I need to calculate the arc length of r(t) = (cost-2)*i + sin2t*j + 2*k from 0 to pi.
I calculated dr/dt= -sint*i + 2cos2t*j
The magnitude of this is sqrt[(-sint)^2 + (2cos2t)^2] if I'm right.
And this is where I'm stuck since I cannot transform this into something that I could integrate on paper. I tried substituting (cost)^2-(sint)^2, 1-2*(sint)^2 or 2*(cost)^2-1 for cos2t but I'm getting nowhere. I feel like I'm missing something here...
Could anyone help me with this?
Thanks,
Evi
Hello,
I need to calculate the arc length of r(t) = (cost-2)*i + sin2t*j + 2*k from 0 to pi.
I calculated dr/dt= -sint*i + 2cos2t*j
The magnitude of this is sqrt[(-sint)^2 + (2cos2t)^2] if I'm right.
And this is where I'm stuck since I cannot transform this into something that I could integrate on paper. I tried substituting (cost)^2-(sint)^2, 1-2*(sint)^2 or 2*(cost)^2-1 for cos2t but I'm getting nowhere. I feel like I'm missing something here...
Could anyone help me with this?
Thanks,
Evi
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