Question

please help me with this problem! in the box I put my answer, however, I got it wrong so if possible, please help me correct whatever my mistake was!

Answer 1

Given

`\sin (2\theta)=(1)/(2)`
`\begin{gathered} 2\theta=sin^(-1)((1)/(2))\text{ } \\ 2\theta=(\pi)/(6) \\ divide\text{ both side by 2} \\ (2\theta)/(2)=(\pi)/(6)/2 \\ \\ \theta=(\pi)/(6)\text{ x }(1)/(2) \\ \\ \theta=(\pi)/(12)\text{ } \end{gathered}`

But sine is also positive in the second quadrant.

Therefore, the solution to the equation also lie in the second quadrant.

Hence,

`\begin{gathered} \theta=\pi-(\pi)/(12) \\ \theta=(12\pi-\pi)/(12) \\ \theta=(11\pi)/(12) \end{gathered}`

The solution of the equation is

`\theta=(\pi)/(12)\text{ and }\theta=(11\pi)/(12)`