Question

Which of the following is an equation for the sine wave graphed below?

Answer 1

Answer:

A $y=8\sin \dfrac{1}{2}x$

Step-by-step explanation:

From the graph you can see that the period of the function is

$720^{\circ}=4\pi$

Now the period of the function $y=8\sin kx$ is

$T=\dfrac{2\pi}{k}$

Thus,

$4\pi=\dfrac{2\pi}{k}\Rightarrow 4\pi k=2\pi\\ \\k=\dfrac{2\pi}{4\pi}=\dfrac{1}{2}$

and the expression for the function is

$y=8\sin \dfrac{1}{2}x$