Question

Find an angle θ, which increases twice as fast as its sine.

Answer 1

$$\begin{gathered} \text{According to the question,} \\ \frac{d\theta }{dt}=2\frac{d}{dt}\left(\sin \theta \right) \\ \Rightarrow \frac{d\theta }{dt}=2\cos \theta \frac{d\theta }{dt} \\ \Rightarrow 2\cos \theta =1 \\ \Rightarrow \cos \theta =\frac{1}{2} \\ \Rightarrow \theta =\frac{\mathrm{\pi }}{3} \end{gathered}$$