Question

3sin(2x)-1=0 to solve

Answer 1

Answer is in the attachment below.

Answer 2

$3\sin (2x)-1=0 \\ \\ 3\sin(2x)=1 \qquad /:3 \\ \\ \sin (2x) = \dfrac{1}{3} \\ \\ 2x=\arcsin \frac{1}{3} +2\pi k\qquad \hbox{or} \qquad 2x= \pi - \arcsin \frac{1}{3}+2\pi k \qquad /:2 \\ \\ x_1=\dfrac{1}{2}\arcsin \frac{1}{3}+\pi k \\ \\ x_2=\dfrac{\pi}{2}-\dfrac{1}{2}\arcsin \frac{1}{3}+\pi k$

k is an integer

arcsin (1/3) is approximately 0.34 radians (19.47 degrees)