When we move our sine or cosine function left or right along the x-axis, we are creating a Horizontal Shift or Horizontal Translation.
In trigonometry, this Horizontal shift is most commonly referred to as the Phase Shift.
As Khan Academy states, a phase shift is any change that occurs in the phase of one quantity.
In other words, there is a change in the phase of our wave.
Typically, this is the trickiest transformation for students to draw because it involves an adjustment to our graphing interval…
…which means dealing with fractions
Horizontal Translation is called the Phase Shift
But don’t worry!
I have an easy, step-by-step approach to graphing any and all types of sine or cosine functions with a phases shift!
So what do we do?
Well, we begin like we always do, and start identifying all the important parts of our function by first getting into our handy-dandy formula.
When we get to dealing with our parentheses, we will notice that we will be either shifting our starting point to the right (positive value) or left (negative value) a specific distance, as appropriately stated by Math Bits Notebook.
Together we will look at each example in detail and learn some easy tricks to help us graph even the most difficult questions.
How to Graph Sine & Cosine (w/ Phase Shift) – Video
Get access to all the courses and over 450 HD videos with your subscription
Monthly and Yearly Plans Available
Still wondering if CalcWorkshop is right for you?
Take a Tour and find out how a membership can take the struggle out of learning math.