Given:
[tex]f(x)=2\sin(3x)[/tex]Required:
To find the period and amplitude of the given function.
Explanation:
Given function is in the form of
[tex]y=a\sin bx[/tex]Here the amplitude is
[tex]=|a|[/tex]Period
[tex]=\frac{2\pi}{b}[/tex]Now consider the given function
[tex]y=2\sin3x[/tex]Here the amplitude is
[tex]\begin{gathered} =|2| \\ =2 \end{gathered}[/tex]And period is
[tex]=\frac{2\pi}{3}[/tex]Final Answer:
The amplitude is 2 and the period is
[tex]\frac{2\pi}{3}[/tex]