Sketch the level curves f(x, y) = c of the following functions for c = −3, −2, −1, 0, 1, 2, and 3:

$f(x,y)=x-{\sin }^{-1}y$

given,

$f(x,y)=x-{\sin }^{-1}y$

Then for $c=-3,y=\sin (x+3)$

Which is the equation of trigonometric sine function with origin shifted to left by 3

For $c=-2,y=\sin (x+2)$

Which is the equation of trigonometric sine function with origin shifted to left by 2
For $c=-1,y=\sin (x+1)$

Which is the equation of trigonometric sine function with origin shifted to left by 1

For $c=0,y=\sin x$

Which is the equation of trigonometric sine function.

For $c=1,y=\sin (x-1)$

Which is the equation of trigonometric sine function with origin shifted to the right by 1
For $c=2,y=\sin (x-2)$

Which is the equation of trigonometric sine function with origin shifted to the right by 2

For $c=3,y=\sin (x-3)$

Which is the equation of trigonometry sin function with origin shifted o right by 3