Chapter 6.4, Problem 4AYU

To determine

To fill: The function y = A sin

(ωx), A>0, has amplitude 3 and period 2; then A = ______ and ω= __________.

Answer to Problem 4AYU

Solution:

3, π

Explanation of Solution

Given:

The function y = A

sin (ωx), A>0, has amplitude 3 and period 2.

Calculation:

If ω>0, the amplitude and period of y = A sin (ωx) and y = A cos (ωx) are given by

Amplitude = |A| Period $T=\frac{2\pi }{\omega }$

Amplitude = |A| = 3.

A = 3

Period $T=\frac{2\pi }{\omega }$ .

  $2=\frac{2\pi }{\omega }$

  $\omega =\pi$

The function $y = A\sin \left(\omega x\right), A>0$ , has amplitude 3 and period 2; then $A = 3$ and $\omega =\pi$ .