Question

Find the amplitude and period of each function then sketch one cycle of the graph of each function.15. y=3 sin 4x 16. y= -2 sin 8x

Answer 1

• Amplitude = 3

,

• Period = π/2

Explanation:

Given the function:

`y=3\sin(4x)`

Compared with the general sine function:

`y=a\sin(bx+c)+d`

We have that:

`\begin{gathered} \text{ Its amplitude}=|a|=3 \\ \text{ Period}=(2\pi)/(|b|)=(2\pi)/(4)=(1)/(2)\pi \end{gathered}`

Next, a sketch of one cycle of the function is given below: