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