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Verifying conservative field

  • #1
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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.
 

Answers and Replies

  • #2
dextercioby
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You should brush up your HS trigonometry before doing anymore maths/physics. How do you expand sin 2y ?
 
  • #3
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Oh.
Is there a way to expand sin2y manually, or is it just one of those things you have to memorize?
 
  • #4
dextercioby
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Trigonometry generally appeals to memory even though some proofs can be visual. sin (x+y) = ? then take x=y.
 
  • #5
[tex]\sin(2y) = 2\sin y \cos y[/tex] for any angle [itex]y[/itex]. So yes, the terms cancel out and the force is conservative.
 

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