(1) On the unit circle, you have \(\sin x=-1\) when \(x=-\dfrac\pi2\), and more generally this is the case whenever you perform a full rotation about the origin. This means \(\sin x=-1\) any time \(x=-\dfrac\pi2+2n\pi\) where \(n\) is any integer.
(2) When \(x=-90^\circ\), you have \(y=f(-90^\circ)=\cos(-90^\circ)=0\).
(3) When \(x=-45^\circ\), you have \(y=f(-45^\circ)=\tan(-45^\circ)=-1\).
(4) The law of sines says that
\(\dfrac{12}{\sin40^\circ}=\dfrac{e}{\sin55^\circ}\implies e\approx15.292\)
(5) The law of cosines says that
\(b^2=6.5^2+8^2-2\times6.5\times8\cos37^\circ\implies b\approx4.816\)
