Is the Given Force Field Conservative?

[leroyjenkens]

Homework Statement

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

Homework Equations

∇xF=0

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.

 

[dextercioby]

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

 

[leroyjenkens]

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

 

[dextercioby]

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

 

[perishingtardi]

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