Question

How do you find the general solutions for `sin x = -1/2`?

Answer 1

Solve `sin x = - 1/2`

Ans: `((7pi)/6) and ((11pi)/6)`

Explanation:

sin (-x) = - sin x = 1/2
Trig Table of Special arcs gives arc `(-x) = - pi/6` (or 30 deg).
Trig unit circle gives another arc `((-5pi)/6)`, that has the same sin value `(-1/2)`
General solutions:
`x = - pi/6 + 2kpi`
`x = - ((5pi)/6) + 2kpi`
You may express the answers by the 2 arcs that have the same terminal
`x = ((7pi)/6) + 2kpi`
`x = ((11pi)/6) + 2kpi`