Question

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

y = 8 sin (1/2x)

y = 8 sin (x)

y = 8 sin (2x)

y = 8 sin (4x)

Answer 1

A
`y=8\sin (1)/(2)x`

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=(2\pi)/(k)`

Thus,

`4\pi=(2\pi)/(k)\Rightarrow 4\pi k=2\pi\\ \\k=(2\pi)/(4\pi)=(1)/(2)`

and the expression for the function is

`y=8\sin (1)/(2)x`