Consider the equation 2 sin x 1 0 Explain the similarities

Consider the equation 2 sin x -1 = 0. Explain the similarities and differences between finding all solutions in the interval [0, pi/2], finding all solutions in the interval [0, 2pi], and finding the general solution.

Solution

2 *sinx-1 = 0;

sinx = 1/2

x =30 degrees or pie/6 radians

if we consider in the interval (0,pie/2) we have only 1 solution pie/6

if we consider the interval (0,2pie) we have 2 solutions namely pie/6 , 5pie/6

general solution is n*pie+- pie/6

n = 1,3,5,7... we should consider -

n = 0,2,4,6,....we should consider +