Q. 1 - Precalculus Enhanced with Graphing Utilities

Question

For the graph of $y=a \sin (\omega x-\varphi )$, the number$\frac{\varphi }{\omega }$is called the                           .

Step-by-Step Solution

Answer

For the graph of $y=a \sin (\omega x-\varphi )$, the number$\frac{\varphi }{\omega }$is called the Phase shift.

Step 1. Given data

The given function is

$y=a \sin (\omega x-\varphi )$

Step 2. Explanation

For Sinusoidal function $$\begin{gathered} y=a \sin (\omega x-\varphi ) \\ \omega >0 \end{gathered}$$

amplitude$=\left|A\right|$

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

Phase shift $=\frac{\varphi }{\omega }$

Where phase shift is left when $\varphi <0$

and the phase shift is right when $\varphi >0$

So for the graph of $y=a \sin (\omega x-\varphi ),$number$\frac{\varphi }{\omega }$ is called the phase shift.