Question

Does anyone know how to graph trigonometric functions for algebra 2?

Answer 1

Give the following below

`\begin{gathered} amplitude=3 \\ period=(\pi)/(2) \\ midline,\text{ }y=-1 \\ Passing\text{ through the point }(0,2) \end{gathered}`

To find the cosine function, we will apply the general formula for cosine function below

`\begin{gathered} f(x)=a\cos(bx-c)+d \\ Where \\ a\text{ is the amplitude} \\ b\text{ represents the speed of the cycle} \\ d\text{ is the vertical shift} \\ (c)/(b)\text{ is the phase shift \lparen horizontal shift\rparen} \\ Period=(2\pi)/(b) \end{gathered}`

To find the value of b

`\begin{gathered} Period=(\pi)/(2) \\ (2\pi)/(b)=(\pi)/(2) \\ Crossmultiply \\ b*\pi=2*2\pi \\ b=(4\pi)/(\pi) \\ b=4 \end{gathered}`
`\begin{gathered} a=3 \\ b=4 \\ d=-1 \\ c=0 \end{gathered}`

Substitute the values of the variables into the general formula for cosine function

`\begin{gathered} f(x)=a\cos(bx-c)+d \\ f(x)=3\cos(4x-0)-1 \\ f(x)=3\cos4x-1 \end{gathered}`

Applying a graphing tool,

The graph of one cycle of the function is shown below