# Why is this equation dimensionally correct?

1. Feb 2, 2012

### Copse

1. The problem statement, all variables and given/known data
Show that this equation is dimensionally correct.
y = (2m)cos(kx), where k = 2m^-1

2. Relevant equations
None that I know of.

3. 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?

2. Feb 2, 2012

### Pengwuino

Yes, trigonometric functions take arguments that are dimensionless.

3. Feb 2, 2012

### Copse

Thank you for answering my question.

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

4. Feb 3, 2012

### vela

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

5. Feb 3, 2012

### Copse

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.

6. Feb 3, 2012

### vela

Staff Emeritus
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.

7. Feb 3, 2012

### 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"!