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Stimpon
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Homework Statement
Homework Equations
[itex]L[c]:=\int_{a}^{b}(\sum_{i,j=1}^{2}g_{ij}(c(t))c_{i}'(t)c_{j}'(t))^{1/2}dt[/itex]
The Attempt at a Solution
So [itex]g_{ij}(x,y)=0[/itex] for [itex]i{\neq}j[/itex], [itex]c_{1}'(t)=-Rsin(t)[/itex], [itex]c_{2}'(t)=Rcos(t)[/itex]
so [itex]L[c]:=\int_{a}^{b}(\frac{1}{((Rsin(t))^{2}}R^{2}(sin^{2}(t)+cos^{2}(t))^{1/2}dt=\int_{a}^{b}\frac{1}{sin(t)}dt[/itex]
However the solutions has
[itex]L[c]:=\int_{a}^{b}(\frac{1}{((Rcos(t))^{2}}R^{2}(sin^{2}(t)+cos^{2}(t))^{1/2}dt=\int_{a}^{b}\frac{1}{cos(t)}dt[/itex]
and he then goes on to use the given identity to find an antiderivative for [itex]\frac{1}{cost}[/itex]
but I don't see how he has cost where I have sint.
Is he making a mistake or am I?
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