- #1

- 111

- 2

[tex] \vec{v} = \frac {d}{dt} (x \hat{i} + y \hat{j}) [/tex]

[tex] = \frac {d}{dt} (rcos \theta) + \frac {d}{dt} (rsin \theta) [/tex]

[tex] = r \frac {d}{dt} (cos \theta) + cos \theta \frac {d}{dt} (r) + r \frac {d}{dt} (sin \theta) + sin \theta \frac {d}{dt} (r)[/tex]

From here on, I get stuck. How do I take the time derivative of [tex]sin \theta[/tex] or other trig functions whose subject is not time? So far, I've got this:

[tex] -r \dot {\theta} sin \theta + \dot{r}cos \theta + r \dot{\theta} cos \theta + \dot{r} sin \theta [/tex]

That being said, I also have a thought that the time-derivative of, say, [tex]sin \theta[/tex] would be zero, because sin(theta) is not dependent upon time. Though, I may be wrong. (Which is entirely why I'm asking here!)

Thanks in advance!