Question

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

Answer 1

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

k is an integer

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

Answer 2

Answer is in the attachment below.