Find the first partial derivative of

[1question]

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?

 

[Simon Bridge]

You have the relation $\sin(\theta)=0:\theta=5y+z$ right ... so what values of $\theta$ make the relation true?

 

[1question]

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

 

[Simon Bridge]

$\sin k\pi=0:k=0,1,2,\cdots$
... sometimes you are staring right at it.