Question

I need help solving for numbers 1 and 2 please! I’ve been stuck on these for a while now.

Answer 1

1) The general form of the cosine function is shown below

`\begin{gathered} f(x)=Acos(B(x+C))+d \\ A,B,C,D\rightarrow\text{ constants} \end{gathered}`

Where B is given by the equation

`\begin{gathered} period=(360\degree)/(B) \\ \end{gathered}`

Thus, in our case,

`\begin{gathered} 120\degree=(360\degree)/(B) \\ \Rightarrow B=3 \end{gathered}`

Therefore, the function is

`\Rightarrow f(x)=cos(3x)`

And its corresponding graph is

Draw the function from the y-axis to the blue line (x=2pi/3=120°)

2)

Similarly, the general form of the sine function is

`\begin{gathered} f(x)=Asin(B(x+C))+D \\ A,B,C,D\rightarrow\text{ constants} \\ A\rightarrow\text{ amplitude} \\ B\rightarrow period=(360\degree)/(B) \end{gathered}`

Thus, in our case, the amplitude of the function is 2 and its period is

`period=(360\degree)/((1)/(5))=1800\degree=10\pi\text{ radians}`

Therefore, the function must repeat itself every 1800° or 10pi radians.

The graph of such function is

Graph from the y-axis to the gray line (x=10pi)