Question

How do you find the general solutions for `sin2x=sqrt3/2`?

Answer 1

Solve `sin 2x = sqrt3/2`

Ans: `pi/3` and `pi/6`

Explanation:

Trig table gives -> `sin 2x = sqrt3/2` --> `2x = (2pi)/3` --> `x = pi/3`
Trig unit circle gives another arc 2x that has the same sine value:
`2x = pi - (2pi)/3 = pi/3` --> `x = pi/6.`
Answer:
`x = pi/3 + 2kpi`
`x = pi/6 + 2kpi`