# Dimensional anaylsis problem involving trigonometry

1. Aug 24, 2013

### mileena

1. The problem statement, all variables and given/known data

Dimensional Analysis:

A displacement is related to time as:

x = A sin (2∏ft), where A and f are constants.

Find the dimensions of A. (Hint: a trigonometric function appearing in an equation must be dimensionless.)

2. Relevant equations

t = seconds
The domain of a sine must be an angle.

3. The attempt at a solution

x = A sin (2∏ft), where A and f are constants.

m = A sin (2∏fs)

A = m/[sin (2∏fs)]

Therefore, f, a constant, must be in terms of s-1, in order to cancel out the s next to it, as the input of sine in an equation must be dimensionless.

Therefore, A = m

Thanks for any help!

2. Aug 24, 2013

### rock.freak667

Yes that would be correct.

3. Aug 24, 2013

### Emilyjoint

Correct

4. Aug 24, 2013

### mileena

I am absolutely stunned that I got the question correct (other than failing to use base dimensions instead of units in the SI system, as Emilyjoint posted in my other thread here!).

Thank you!