Is the Curl of This Vector Field Zero?

[mathwizeguy]

Homework Statement

F=-ysin(x)i+cos(x)j

Homework Equations

Can the Curl test be applied to this vector field and state three facts you can deduce after applying the curl test.

The Attempt at a Solution

 

[psholtz]

What exactly do you mean by "curl test"?

 

[mathwizeguy]

the curl test is a test to find if a vector field is path independent by taking the partial derivative of F1 and F2 of a function F with respect to x, for F2, and with respect to y, for F1.

Basically I am havin trouble finding 3 facts to incur about this F after the curl test.

 

[psholtz]

Are you able to find the curl of this vector field?

In general, if the curl of a vector field is zero, that means that (a) it's the gradient of a scalar (potential) function; and (b) the line integral of scalar potential function is path-independent.