Question

The answe to a) is 180and the answe to b) is 2i need help with c

Answer 1

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

`\begin{gathered} A=2 \\ Period=270^0-90^0=180^0 \\ Period=(2\pi)/(B) \\ \pi=180^0 \\ 180^0=(2*180^0)/(B) \\ B*180^0=360^0 \\ B=(360^0)/(180^0) \\ B=2 \end{gathered}`
`\begin{gathered} C=phase(shift)=-45^0 \\ D=-3 \end{gathered}`

So, the function of the graph would be

`\begin{gathered} y=Asin(B(x+C))+D \\ A=2 \\ B=2 \\ C=-45^0 \\ D=-3 \end{gathered}`
`\begin{gathered} f(x)=2sin(2(x-45^0)-3 \\ f(x)=2sin(2x-90^0)-3 \end{gathered}`
`\begin{gathered} OR \\ f(x)=2sin(2x-(\pi)/(2))-3 \end{gathered}`

Hence, the sine function of the given graph is

y = 2sin(2x - 90⁰) - 3

OR

y = 2sin(2x - π/2) - 3