Page:Calculus Made Easy.pdf/189

 Now remember that if $$d\theta$$ is indefinitely diminished, the value of $$\tan d\theta$$ becomes identical with $$d\theta$$, and $$\tan \cdot d\theta$$ is negligibly small compared with $$1$$, so that the expression reduces to

Collecting these results, we have: Sometimes, in mechanical and physical questions, as, for example, in simple harmonic motion and in wave-motions, we have to deal with angles that increase in proportion to the time. Thus, if $$T$$ be the time of one complete period, or movement round the circle, then, since the angle all round the circle is $$2\pi$$ radians, or $$360^\circ$$, the amount of angle moved through in time $$t$$, will be