Answer:
y=2cos(x-30)+2
Explanation:
The general form of the cosine function is given:
[tex]\begin{gathered} y=A\cos (B(x+C))+D \\ A=\text{Amplitude} \\ Period,T=\frac{2\pi}{B}=\frac{360}{B}(in\text{ degr}ees) \\ C=\text{Phase Shift} \\ D=\text{Vertical Shift} \end{gathered}[/tex]Find the value of A using the maximum value.
[tex]A=\frac{1}{2}\times4=2[/tex]The period of the graph is 360 degrees. B is calculated below:
[tex]\begin{gathered} \frac{2\times180}{B}=360 \\ 360B=360 \\ B=1 \end{gathered}[/tex]If Phase shift = 30 degrees (to the right)
[tex]C=-30[/tex]Vertical Displacement = 2 units up
[tex]D=2[/tex]The period of the graph is calculated below:
[tex]\begin{gathered} \frac{2\times180}{B}=360 \\ 360B=360 \\ B=1 \end{gathered}[/tex]Thus, the graph with the given properties is:
[tex]y=2\cos \mleft(x-30\mright)+2[/tex]
