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

$\begin{gathered} period=\frac{360\degree}{B} \\ \end{gathered}$

Thus, in our case,

$\begin{gathered} 120\degree=\frac{360\degree}{B} \\ \Rightarrow B=3 \end{gathered}$

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

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

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

$period=\frac{360\degree}{\frac{1}{5}}=1800\degree=10\pi\text{ radians}$

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)