Solution:
The sine function is generally expressed as
[tex]\begin{gathered} y=A\sin(B(x+C))+D\text{ ---- equation 1} \\ where \\ A\Rightarrow amplitude \\ C\Rightarrow phase\text{ shift} \\ D\Rightarrow vertical\text{ shift} \\ \end{gathered}[/tex]
The period of the function is expressed as
[tex]period=\frac{2\pi}{B}[/tex]
Given the function:
[tex]y=\sin((\frac{7\pi}{4}x))\text{ ---- equation 2}[/tex]
Comparing equations 1 and 2, we see that
[tex]B=\frac{7\pi}{4}[/tex]
Thus, by substituting the value of B into the period formula, we have
[tex]\begin{gathered} period=\frac{2\pi}{\frac{7\pi}{4}} \\ =2\pi\times\frac{4}{7\pi} \\ =\frac{2\times\text{4}}{7} \\ =\frac{8}{7} \end{gathered}[/tex]
Hence, the period of the function is
[tex]\frac{8}{7}[/tex]
