Answer
a) $\theta=0.6245+\dfrac{\pi k}{2}$
b) $\theta =0.6245$radians ; $\theta =2.195$radians ; $\theta =3.766$radians ; $\theta =5.337$radians
Work Step by Step
a) $\sin 2 \theta=3 \cos 2\theta$
or, $\dfrac{\sin 2 \theta}{\cos 2\theta}=\dfrac{3 \cos 2\theta}{\cos 2\theta}$
This gives: $\tan 2\theta=3 \implies 2\theta=1.249+\pi k$
Thus, $\theta=0.6245+\dfrac{\pi k}{2}$
b) In order to get the solutions in the interval $[0,2 \pi)$, we will have to put $k=0,1,2,3$, because the other values will make $\theta \gt 2 \pi$
Thus, we have $\theta =0.6245$radians for $k=0$
$\theta =2.195$radians for $k=1$
$\theta =3.766$radians for $k=2$
$\theta =5.337$radians for $k=3$
