Find all the real numbers thar satisfy the equation hint pi

Find all the real numbers thar satisfy the equation ... hint (pie form +k)

sin 2x = -1/2

Solution

We have given sin 2x=-1/2

2x=arcsin(-1/2)

2x=7pi/6 or 2x=11pi/6

x=7pi/12 or x=11pi/12

sinx period is 2pi which implies sin2x period is 2pi/2=pi

x=(7pi/12)+k,(11pi/12)+k, k belongs to z