What units will the partial derivative of an angular equation give?

[jeffyhow]

Homework Statement

If I have an equation that describes L in terms of some constants and an angle.

e.g. L=C1*\sqrt{(C2-Sin[angle])}+C1*\sqrt{(C2-Cos[angle])}

Then, if I take the partial derivative of the above wrt angle, then I would get the unit change in L for a unit change in angle.

However, if I solve the partial derivative at a specific angle, will it give me units of length/degrees or units of length/radians?

The above equation is just an example of one case for the my question.

 

[Dick]

Hard to say with without a context, but probably radians. If you say the derivative of sin(x) is cos(x), then x is in radians. If your angle x is represented in degrees then the derivative of sin(x) is cos(x)*pi/180.

 

[HallsofIvy]

Trig functions (as opposed to values you would use to solve right triangle problems) don't necessairily have anything to do with angles. They are defined in such a way that if you are treating the variables as angles, they would have to be in radians.

I'm not sure why you are talking about "partial derivatives"- there are no partial derivatives. The only independent variable is "angle" so you only need an ordinary derivative.

 

[Smartass]

Depends on how you integrate. If you are taking derivative of six=cosx, then x will be in radians, ie, you answer will be in lenght/rad. Oh and partial derivative, as HallsofIvy said, is not necessary, as only a single variable is involved.