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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?