Question

Question #fd3e2

Answer 1

half close intervals: `(0, pi/6]` and `[(5pi)/6, 2pi)`

Explanation:

`9sin x <= 9/2`
`sin x <= 1/2`
Trig table gives 2 arcs `x = pi/6` and `x = (5pi)/6`
that have the same sin value (1/2)
Use the unit circle to solve the above trig inequality.
`sin x < 1/2`, when x varies on the unit circle, inside the half closed intervals:
`[(5pi)/6, 2pi)` and `(0, pi/6]`
Note. The sign `<=` explains the half closed intervals. That means the arcs `(pi/6)` and `(5pi)/6` are included in the solution set.