Question

Question #57bde

Answer 1

`(7pi)/6 + 2kpi`
`(11pi)/6 + 2kpi`

Explanation:

`sin^-2 (1/2) --> arcsin (-1/2)`
Trig table of special arcs and unit circle give:
`sin x = - 1/2` --> arc `x = - pi/6 + 2kpi` and
arc `x = pi + pi/6 = (7pi)/6 + 2kpi`
Because the arc `pi/6` is co-terminal to `(11pi)/6`, then, the answers are:
`x = (7pi)/6 + 2kpi`
`x = (11pi)/6 + 2kpi`