Q:

Really simple question about sine wave equation with $\pi$

I'm reading some EE material, and my trigonometry is really rusty.
There is an equation that looks like:
$y(t) = \sin(2\pi \times 150 \times t)$
Why is there a $2\pi$ factor in the argument?
When I learned trig (many, many years ago), I learned equations that look like:
$y(t) = \sin(150  t)$
where the $150$ was assumed to be in radians already.
Are these the same equation, and if so, when would I use one form but not the other?

A:

It is just a matter of units of measure. In $u(t)=\sin(\omega t)$, $\omega$ is an angular frequency, that is radians per unit time. In $v(t)=\sin(2\pi \nu t)$, $\nu$ is a frequency, that is number of cycles per unit time.

