1) The general form of the cosine function is shown below
[tex]\begin{gathered} f(x)=Acos(B(x+C))+d \\ A,B,C,D\rightarrow\text{ constants} \end{gathered}[/tex]
Where B is given by the equation
[tex]\begin{gathered} period=\frac{360\degree}{B} \\ \end{gathered}[/tex]
Thus, in our case,
[tex]\begin{gathered} 120\degree=\frac{360\degree}{B} \\ \Rightarrow B=3 \end{gathered}[/tex]
Therefore, the function is
[tex]\Rightarrow f(x)=cos(3x)[/tex]
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
[tex]\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}[/tex]
Thus, in our case, the amplitude of the function is 2 and its period is
[tex]period=\frac{360\degree}{\frac{1}{5}}=1800\degree=10\pi\text{ radians}[/tex]
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)
