Is y=(2m)*cos(k*x) dimensionally correct, where k = 2m^-1?

This question is from Chapter 1.4, "Dimensional Analysis" of Serway's Physics (4th Edition). It comes from homework problem 13.b

1 Answer
Mar 18, 2016

No, it is not dimensionally correct.

Explanation:

Let m = L for length
Let k = 2/L for the given m^-1
Let x remain an unknown variable. Plugging these into the original equation gives us:

y=(2L)*cos(2/L*x)

Letting the dimensions absorb the constants, we have

y=(L)*cos(x/L)

This puts units inside of a cosine function. However, a cosine function will simply output a non-dimensional value between +-1, not a new dimensional value. Therefore, this equation is not dimensionally correct.