Amplitude, Period, Phase Shift, Vertical Shift, and Frequency - Problem 1

Given the equation y = 2 sin (4x − 0.5) + 3.

Find the following:

• Amplitude 
• Period 
• Phase Shift 
• Vertical Shift 
• Frequency 

Solution:

\begin{equation} A = 2 \end{equation}

Answer: \begin{equation} A = 2 \end{equation}

\begin{equation} P = \frac{2 \pi}{B} \end{equation}

\begin{equation} P = \frac{2 \pi}{4} \end{equation}

\begin{equation} P = \frac{\pi}{2} \end{equation}

Answer: \begin{equation} P = \frac{\pi}{2} \end{equation}

\begin{equation} C = -0.5 \end{equation}

Answer: \begin{equation} C = -0.5 \end{equation} or 0.5 unit shifted to the right

\begin{equation} D = 3 \end{equation}

Answer: \begin{equation} D = 3 \end{equation} or 3 units shifted upward

\begin{equation} F = \frac{1}{P} \end{equation}

\begin{equation} F = \frac{1}{\frac{\pi}{2}} \end{equation}

\begin{equation} F \approx 0.637 \end{equation}

Answer: \begin{equation} F = 0.637 \end{equation}