ahh thank you makes so much sense now! i have another problem and if u could help me with it plz,

so i want to find the exact solutions to the problem,

sin2x=sprt3/2 for the interval 0</= x </=2pi

and by finding the inverse sine i find it being pi/3 and by solving for x i get also pi/6 those are the two first exact solutions now since its a positive square root thus we are looking for where sine is positive which means that the other solutions are 2pi/3 and 5pi/6 however according to the book that is wrong and the answer is pi/3, pi/6, 7pi/4, and 4pi/3, how could this be?!