From where does this - ve sign come from

Question

Let
θ=54
5θ=270
2θ+3θ=270
2θ=270-3θ
sin(2θ)=sin(270-3θ)
sin(2θ)= -cos(3θ)
From where does -ve sign come from?

270-3θ will be in 2quad where sin is +ve.

Answer 1

\begin{align} \sin (270^\circ-\alpha) &= \sin(270^\circ)\cos(\alpha) -\cos(270^\circ) \sin(\alpha) \\ &=- \cos (\alpha) \end{align}

Answer 2

$\sin(-90^\circ -\alpha) = \cos(\alpha)$ for any $\alpha$