You're good.

Let us continue,

sin(alpha) = (-6/sqrt(52))

Rationalize the denominator,

= (-6/sqrt(52)*sqrt(52)/sqrt(52)

= -6(sqrt(13*2*2) / 52)

Get the 2*2 out of the sqrt sign,

= -6[2sqrt(13)] / 52

= -12[sqrt(13)] / 52

Reduce it to its lowest term, divide both numerator and denominator by 4,

= -3[sqrt(13)] / 13 ----------answer.