(b) A distance is related to time according to the expression x = A sin(2πft), where A and f are constants. Find the dimensions of A. Again, "L" is the length dimension and "T" is the time dimension. [Hint: A trigonometric function appearing in an equation must be dimensionless.]

A is in  length dimensions

Step-by-step explanation:

The expression:

x  =  A sin (2πft)

has in the second member two factors   A   and sin (2πft); a sine is a relation between two sides with the same dimension that means a sine is a number ( with minimum and maximum values of 0 for zero degrees and 1 for 90 degrees ). As t is in units of time ( seconds, minutes or hours) frequency "f", which is the number of cycles per unit of time       ( seconds, minutes or hours), t  and f should be both in the same unit, in order to get just a number for sin2πf.

Therefore A should be in units of length and x will get its units from A

For instance

x = A sin(2πft)  

t in seconds          f  in 1/seconds        A in meters

By substitution, we can see that

x[ m ]  = A [m] * sin[ 2π*sec* 1/sec ]

x[ m ]  = A [m] * number

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step-by-step explanation:

step-by-step explanation: