ayame
26

# Need some help with these last few problems Thank you for your time and help 1. For what x-value(s) does sin(x) = -1? 2. What is the y-value for f(x) = cos(x) when x = -90°? 3. What is the y-value for f(x) = tan(x) when x = -45°? 4. Find the value of e. ( Left Image ) 5. Find the value of b. ( Right Image )

jackie1977

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