Question

sin2x = 1/4

Answer 1

over in interval 0, 2pi

Answer 2

To solve for x, take the arcsin of 1/4. By taking the arcsin, we switch what is in the sin (in our case, 2x) with what is on the other side of the equation. Based on the equation you provided, this will give us:
\[\sin^{-1} 1/4 = 2x\]
Arcsin denotes at what radian sine will be 1/4 in the unit circle. The question was not about unit circles, so I won't go to much into that. Using a typical TI - 84, we would press 2nd -> sin to get the arcsin. Entering 1/4, we get .2527 (Make sure you are in radian mode, unless you are looking for the degree. I will be using radian mode, as that it what is typically used.) So, the sin of radian .2527 is 1/4. Now we have:
\[.2527 = 2x\]
Since we're not done with the problem yet, don't round off your numbers. 4 decimal points is usually a good number to keep it at. All we have to do now is divide both sides by 2:
\[.2527\div 2 = 2x\div 2\]
\[.1263 = x\]
Congrats! We found x. Hope this helps :)