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