If theta is considered small in problems

[M. next]

we know when theta is considered small enough, sin(theta) is approximately equal to theta. Ok, the question is what happens to theta dot(the time derivative of theta)?

 

[mfb]

If $\theta$ is small all the time, the time-derivative of $sin(\theta)$ is approximately the time-derivative of $\theta$.

 

[M. next]

thanks

 

[Nabeshin]

Another way of seeing the above is that the time derivative of sin is cosine, and when theta is small cosine is approximately equal to one.