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I'm trying to figure out what the b-value is called? y=sin(bx)

I've heard some say that it's the frequency or angular frequency, but if my x-values are radian values and not time then what would "b" be called?

Angular frequency seems more accurate than frequency. In my understanding, angular frequency, or angular speed, is the number of radians per second. And frequency is the number of cycles per second. But those are both per a time unit which means that "b" must be a unit of time. But my x value is the number of radians.

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$b$ is a unit-less real number (as is $x$, technically). The period of the sine function is $2\pi/b$. – NotNotLogical May 20 '14 at 2:28
up vote 2 down vote accepted

It's still frequency. The concept is the same, regardless of whether $x$ is a dimensionless quantity or not.

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I think a physicist would call it 'the frequency divided by two pi'. – Ruben May 20 '14 at 3:03
Frequency multiplied by two pi – TylerHG May 20 '14 at 3:04
I think that multiplying anything by a constant rarely, if ever, changes its underlying meaning. – Emily May 20 '14 at 3:40
The answer and comments seem to confirm my issue with defining the name of the b value. I thought there might be more of a consensus. – tazboy May 20 '14 at 14:58
I don't think so. Some people insist that frequency be a multiple of $2\pi$, but this is ridiculous. In the equation $y=mx+b$, $m$ represents the slope regardless of what the units and scaling are. We don't call it something different if all of a sudden we want to re-scale $x$ to be on the order of parsecs or somesuch. – Emily May 20 '14 at 15:04

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