Question

How do you solve `sin x = -1/2`?

Answer 1

Solution is x=`(7pi)/6`, `(11pi)/6` in (0,2pi), or in general
`x= nπ+(−1)^n(−π/6)`, n is any integer

Explanation:

sinx = `-1/2` for x=`(7pi)/6`, `(11pi)/6` in (0,2pi), that is in IIIrd and IVth quadrant. For a general solution go on adding `2pi` in both these values which can be written as x= `n pi +(-1)^n (-pi/6)`, n is any integer