Question

I need help on this please! Assignment is called “Periods and Amplitudes” not sure if that helps lol

Answer 1

The sine function is generally expressed as

`\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}`

The period of the function is expressed as

`period=(2\pi)/(B)`

Given the function:

`y=\sin(((7\pi)/(4)x))\text{ ---- equation 2}`

Comparing equations 1 and 2, we see that

`B=(7\pi)/(4)`

Thus, by substituting the value of B into the period formula, we have

`\begin{gathered} period=(2\pi)/((7\pi)/(4)) \\ =2\pi*(4)/(7\pi) \\ =\frac{2*\text{4}}{7} \\ =(8)/(7) \end{gathered}`

Hence, the period of the function is

`(8)/(7)`