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

Answer:

• 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:

$\begin{gathered} \text{ Its amplitude}=|a|=3 \\ \text{ Period}=\frac{2\pi}{|b|}=\frac{2\pi}{4}=\frac{1}{2}\pi \end{gathered}$

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