Answer:
• Amplitude: 3
,
• Period: π/2
,
• Phase Shift: 1/8 (to the left)
,
• Vertical Shift: -0.5
Explanation:
Given the trigonometric function:
[tex]y=3\sin (4x+\frac{1}{2})-0.5[/tex]
Comparing with the form below:
[tex]\begin{gathered} y=A\sin (Bx-C)+D\text{ where:} \\ \text{Amplitude}=A \\ Period=\frac{2\pi}{B} \\ Phase\text{ Shift}=\frac{C}{B} \\ \text{Vertical Shift}=D \end{gathered}[/tex]
Thus, we have that:
[tex]\begin{gathered} \text{Amplitude,}A=3 \\ Period,\frac{2\pi}{B}=\frac{2\pi}{4}=\frac{\pi}{2} \\ Phase\text{ Shift,}\frac{C}{B}=-\frac{1}{2}\div4=-\frac{1}{8} \\ \text{Vertical Shift, }D=-0.5 \end{gathered}[/tex]
The phase shift, -1/8 indicates a shift to the left.
