Question

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 )

Answer 1

(1) On the unit circle, you have
`\sin x=-1` when
`x=-\frac\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=-\frac\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


`(12)/(\sin40^\circ)=(e)/(\sin55^\circ)\implies e\approx15.292`

(5) The law of cosines says that


`b^2=6.5^2+8^2-2*6.5*8\cos37^\circ\implies b\approx4.816`