SOLUTION:
Case: Period and Amplitude
Method:
a) The period of the function
[tex]g(x)=cos(\frac{x}{3})[/tex]
Compared to the standard
[tex]\begin{gathered} T=\frac{2\pi}{\frac{1}{3}} \\ T=6\pi \end{gathered}[/tex]
The Period,
[tex]T=6\pi[/tex]
b)
[tex]\begin{gathered} f(x)=\frac{1}{2}sinx \\ Amplitude \\ A=\frac{1}{2} \end{gathered}[/tex]
Because the amplitude A is a fraction, it is a vertical compression
Final answers:
[tex]\begin{gathered} Period,T=6\pi \\ Amplitude,A=\frac{1}{2} \\ Compressed\text{ }Vertically \end{gathered}[/tex]
