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
Andy Y.
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.

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