Question

Need some help with these last few problems Thank you for your time and help

Answer 1

(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

$b^2=6.5^2+8^2-2\times6.5\times8\cos37^\circ\implies b\approx4.816$