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Find the first partial derivative of

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Homework Statement



Find the first partial derivatives ∂z/∂x and ∂z/∂y of sin(0x+5y+z)=0 at (0,0,0).

Homework Equations



sin(0x+5y+z)=0


The Attempt at a Solution



0x+5y+z=kπ
z=kπ-5y

So,

∂z/∂x= 0 and ∂z/∂y= -5

What I do not understand is WHY 0x+5y+z=kπ is an acceptable equation. I found it from a solution of this online, but with no explanation. What is the significance of k and π, and why can we basically ignore the sin?
 

Answers and Replies

  • #2
Simon Bridge
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You have the relation ##\sin(\theta)=0:\theta=5y+z## right ... so what values of ##\theta## make the relation true?
 
  • #3
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You have the relation ##\sin(\theta)=0:\theta=5y+z## right ... so what values of ##\theta## make the relation true?
Oh, duh! Sin(0)=0.

Thanks
 
  • #4
Simon Bridge
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##\sin k\pi=0:k=0,1,2,\cdots##
... sometimes you are staring right at it.
 

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