Question

Find an angle $\theta ,0<\theta <\frac{\pi }{2}$, which increases twice as fast as its sine.

Answer 1

Let $\theta$ increases twice as fast as its sine.

$\frac{d\theta }{dt}=2\frac{d\left(\sin \theta \right)}{dt}$

$\frac{d\theta }{dt}=2\cos \theta \frac{d\theta }{dt}$

$1=2\cos \theta$

$\cos \theta =\frac{1}{2}$

$\theta =\frac{\pi }{3}$