Question

How do you find all solutions to the equation `sin2x=-sqrt3/2`?

Answer 1

`(5pi)/6 + kpi`
`(2pi)/3 + kpi`

Explanation:

`sin 2x = - sqrt3/2`
Trig table and unit circle give 2 solutions:
`2x = - (pi)/3 + 2kpi`, or `2x = (5pi)/3 + 2kpi`, (co-terminal)
`2x = - (2pi)/3 + 2kpi`, or `2x = (4pi)/3 + 2kpi` (co-terminal)
a. `2x = (5pi)/3 + 2kpi` --> `x = (5pi)/6 + kpi`
b. `2x = (4pi)/3 + 2kpi` -->`x = (4pi)/6 + kpi = (2pi)/3 + kpi`