Question

Can someone tell me how this happened?

Answer 1

It is marked in red, how did that -sqrt(19)/10 appear?

Answer 2

Because they took the square root of both sides.

Answer 3

\[\sin^2(x) = (\sin(x))^2\]

Answer 4

\[\Large \sin^2t \quad=\quad \frac{19}{100}\]Taking the square root of each side gives us,\[\Large \sin t\quad=\quad \pm\frac{\sqrt{19}}{10}\]

So is your question, `why did they choose the negative root`?