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.

Results 1 to 10 of 10

- Dec 16th 2010, 08:27 AM #1

- Joined
- Jan 2010
- Posts
- 72

- Dec 16th 2010, 12:38 PM #2

- Joined
- Apr 2005
- Posts
- 18,452
- Thanks
- 2535

- Dec 16th 2010, 12:56 PM #3

- Joined
- Jan 2010
- Posts
- 72

- Dec 16th 2010, 01:34 PM #4

- Joined
- Dec 2010
- Posts
- 470

- Dec 16th 2010, 01:42 PM #5

- Joined
- Jan 2010
- Posts
- 72

- Dec 16th 2010, 01:51 PM #6

- Joined
- Dec 2010
- Posts
- 470

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).

- Dec 16th 2010, 03:34 PM #7

- Dec 17th 2010, 02:37 AM #8

- Joined
- Apr 2005
- Posts
- 18,452
- Thanks
- 2535

- Dec 17th 2010, 04:54 AM #9

- Joined
- Jan 2010
- Posts
- 72

- Dec 17th 2010, 06:03 AM #10