Given: The sine graph shown in the image
To Determine: The amplitude, the period and the sine function
Solution
The general sine function is as shown below
From the given graph,
The amplitude is
[tex]\begin{gathered} A=2 \\ Period=270^0-90^0=180^0 \\ Period=\frac{2\pi}{B} \\ \pi=180^0 \\ 180^0=\frac{2\times180^0}{B} \\ B\times180^0=360^0 \\ B=\frac{360^0}{180^0} \\ B=2 \end{gathered}[/tex][tex]\begin{gathered} C=phase(shift)=-45^0 \\ D=-3 \end{gathered}[/tex]
So, the function of the graph would be
[tex]\begin{gathered} y=Asin(B(x+C))+D \\ A=2 \\ B=2 \\ C=-45^0 \\ D=-3 \end{gathered}[/tex][tex]\begin{gathered} f(x)=2sin(2(x-45^0)-3 \\ f(x)=2sin(2x-90^0)-3 \end{gathered}[/tex][tex]\begin{gathered} OR \\ f(x)=2sin(2x-\frac{\pi}{2})-3 \end{gathered}[/tex]
Hence, the sine function of the given graph is
y = 2sin(2x - 90⁰) - 3
OR
y = 2sin(2x - π/2) - 3
