Why is this equation dimensionally correct?

[Copse]

Homework Statement

Show that this equation is dimensionally correct.
y = (2m)cos(kx), where k = 2m^-1

Homework Equations

None that I know of.

The Attempt at a Solution

I don't know why this is correct. I have looked through the chapter and all of the dimensional analysis examples(there are only three) list what the variables represent. The only information given is what I have typed, so I am just assuming that m represents meters.

Are trig. functions dimensionless?

 

[Pengwuino]

Yes, trigonometric functions take arguments that are dimensionless.

 

[Copse]

Yes, trigonometric functions take arguments that are dimensionless.

Thank you for answering my question.

So, does it just boil down to the equation being correct because y and 2m are both lengths?

 

[vela]

Were you asking if kx is dimensionless or if cos kx is dimensionless?

 

[Copse]

Were you asking if kx is dimensionless or if cos kx is dimensionless?

cos(kx)
This is my first physics class and our book doesn't mention trig. functions in the section about dimensional analysis. I am just a little confused.

 

[vela]

OK, Pengwuino answered the other question: kx needs to be dimensionless. The value of the cosine is dimensionless as well, which is the answer to your question.

In general, the standard mathematical functions map a unitless quantity to a unitless result. The main exception is the logarithm because you can do things like log (a/b) = log a - log b, but you should be able to combine logarithms in a way so that you have a unitless argument.

 

[HallsofIvy]

Actually, whether this is "dimensionally correct" depends upon what dimensions x has!

Assuming that x is a distance, measured in meters, then, since k has dimensions of "m^{-1}", kx is dimensionless. In general, mathematical functions take dimensionless variables and return dimensionless values. When you are told that $f(x)= x^2$ and asked "what is f(3)", you don't have to ask if it is 3 meters or 3 feet, the answer is "9"!