Essentially, you want to solve the twonon-linearequations x= u+ sin v, y= v+ cos u for u and v in terms of x and y. I doubt that there will be any elementary solution for that.

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- December 16th 2010, 07:27 AM #1

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- December 16th 2010, 11:38 AM #2

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- December 16th 2010, 11:56 AM #3

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- December 16th 2010, 12:34 PM #4

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- December 16th 2010, 12:42 PM #5

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- December 16th 2010, 12:51 PM #6

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Right, so you don't actually need the explicit formula.

For example, to find and .

Take the partials of the equations directly (independent variables are ):

Note that and .

Solve this system of linear equations at the given point for .

Similar process for other derivatives.

Note you do need to solve for u and v at the point , and you use these values when evaluating things like sin(u).

- December 16th 2010, 02:34 PM #7

- December 17th 2010, 01:37 AM #8

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- December 17th 2010, 03:54 AM #9

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- December 17th 2010, 05:03 AM #10