Question

The amplitude A and period T of$f\left(x\right)=5\sin \left(4x\right)$ are ____ and ____ .

Short answer

The amplitude and period of$f\left(x\right)=5\sin \left(4x\right)$are$5and\frac{\pi }{2}$

Step-by-step solution

Given information

We are given an equation$f\left(x\right)=5\sin \left(4x\right)$

Compare with standard equation and find amplitude and time period

The standard equation is $f\left(x\right)=A\sin \left(\omega x\right)$

comparing with standard equation we get,

$$\begin{gathered} A=5 \\ \omega =4 \end{gathered}$$

Now

$$\begin{gathered} \omega =\frac{2\pi }{T} \\ 4=\frac{2\pi }{T} \\ T=\frac{2\pi }{4} \\ T=\frac{\pi }{2} \end{gathered}$$

Conclusion

The amplitude and time period of$f\left(x\right)=5\sin \left(4x\right)$is$5and\frac{\pi }{2}$