Given
[tex]y=\frac{1}{2}\cdot\sin(4\theta)[/tex]
Find
Amplitude and period of the function and graph it.
Explanation
the amplitude of the function is the largest value that the given function may attain. the amplitude of the given function is 1/2.
to find the period of the function , divide 2pi by the coefficient of theta
here , the coefficient of theta is 4 .
so , the period =
[tex]\begin{gathered} \frac{2\pi}{4} \\ \\ \frac{\pi}{2} \end{gathered}[/tex]
given function has an amplitude of 1/2 and period of pi/2.
now , we graph the function.
the graph completed one period in the interval
[tex]0\leq\theta\leq\frac{\pi}{2}[/tex]
that an effect of shrinking the graph horizontally,
Final Answer
The graph will be made as shown
