Question

Choose the equation that describes the graph with the following properties. A period of 360 degrees. A phase shift of 30 degrees to the right. A vertical displacement of 2 units up. A Maximum value of 4. y= 2cos(2(x-30))+2y=2sin(x+30)+2y=2cos(x-30)+2y=4sin(x-30)+2None of the Above

Answer 1

y=2cos(x-30)+2

Step-by-step explanation:

The general form of the cosine function is given:

`\begin{gathered} y=A\cos (B(x+C))+D \\ A=\text{Amplitude} \\ Period,T=(2\pi)/(B)=(360)/(B)(in\text{ degr}ees) \\ C=\text{Phase Shift} \\ D=\text{Vertical Shift} \end{gathered}`

Find the value of A using the maximum value.

`A=(1)/(2)*4=2`

The period of the graph is 360 degrees. B is calculated below:

`\begin{gathered} (2*180)/(B)=360 \\ 360B=360 \\ B=1 \end{gathered}`

If Phase shift = 30 degrees (to the right)

`C=-30`

Vertical Displacement = 2 units up

`D=2`

The period of the graph is calculated below:

`\begin{gathered} (2*180)/(B)=360 \\ 360B=360 \\ B=1 \end{gathered}`

Thus, the graph with the given properties is:

`y=2\cos \mleft(x-30\mright)+2`