Answer:
Amplitude of the function is 4, period of the function is π and phase shift of the function is [tex]-\frac{\pi}{2}[/tex].
Step-by-step explanation:
The given function is
[tex]f(x)=-4\sin(2x+\pi)-5[/tex] .... (1)
The general form of a sine function is
[tex]f(x)=A\sin(Bx+C)+D[/tex] .... (2)
where, |A| is amplitude, [tex]\frac{2\pi}{B}[/tex] is period, [tex]-\frac{C}{B}[/tex] is phase shift and D is midline.
From (1) and (2) we get
[tex]A=-4,B=2, C=\pi,D=-5[/tex]
[tex]|A|=|-4|=4[/tex]
Amplitude of the function is 4.
[tex]\frac{2\pi}{B}=\frac{2\pi}{2}=\pi[/tex]
Period of the function is π.
[tex]-\frac{C}{B}=-\frac{\pi}{2}[/tex]
Therefore the phase shift of the function is [tex]-\frac{\pi}{2}[/tex].