# Verifying conservative field

1. Oct 7, 2013

### leroyjenkens

1. The problem statement, all variables and given/known data

Verify the following force field is conservative.
F = 2xcos2yi - (x2+1)sin2yj

2. Relevant equations

∇xF=0

3. The attempt at a solution
I'm pretty sure this is just a mistake in the book, but according to my calculations, this isn't a conservative force.
I used the determinant method to do the curl of F to find -2xsin(2y) + 4xsinycosy. Unless those two terms cancel each other to equal 0, then the force isn't conservative and there's a mistake in the book.

What do you think? Thanks.

2. Oct 7, 2013

### dextercioby

You should brush up your HS trigonometry before doing anymore maths/physics. How do you expand sin 2y ?

3. Oct 7, 2013

### leroyjenkens

Oh.
Is there a way to expand sin2y manually, or is it just one of those things you have to memorize?

4. Oct 7, 2013

### dextercioby

Trigonometry generally appeals to memory even though some proofs can be visual. sin (x+y) = ? then take x=y.

5. Oct 8, 2013

### perishingtardi

$$\sin(2y) = 2\sin y \cos y$$ for any angle $y$. So yes, the terms cancel out and the force is conservative.