# 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

Mar 18, 2016

No, it is not dimensionally correct.

#### Explanation:

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

$y = \left(2 L\right) \cdot \cos \left(\frac{2}{L} \cdot x\right)$

Letting the dimensions absorb the constants, we have

$y = \left(L\right) \cdot \cos \left(\frac{x}{L}\right)$

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