Has my teacher been wrong here

[nabliat]

http://i28.tinypic.com/qz54aw.jpg

he reduced 2 points
and put s on the numerator making it cosine formula.
also i clearly transformed sinus

 

[CompuChip]

Probably it is because
$$\sin(t) = -\cos(t - 3\pi / 2)$$
and not
$$-\sin(t - 3\pi / 2)$$