How Do You Horizontally Translate a Trigonometric Graph?

Note:

Translating a graph of sine or cosine horizontally can be fun, but you need to understand how it works. Follow along with this tutorial to learn how to horizontally shift the sine and cosine graphs!

Keywords:

definition
horizontal translation
sine cosine
trigonometric function
horizontal shift
right shift
left shift
phase shift
phase

Background Tutorials

Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.
- How Do You Subtract a Negative Number from a Positive Number?
  
  Subtracting a negative from a positive? Just remember: subtracting a negative is the same as adding a positive. See how it works in this tutorial!
Lines are taken to lines, and line segments to line segments of the same length.
- What is a Translation?
  
  Ever slide something across a table? If so, then you have performed a translation! In this tutorial, learn the definition of translation and see some really neat examples. Take a look!
Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
- What Does the Graph of the Cosine Function Look Like?
  
  You can use the unit circle to help you graph the cosine function! In this tutorial, you'll learn how to do exactly that!
- What is a Periodic Function?
  
  Periodic functions have some special qualities! In this tutorial, you'll be introduced to these functions and learn what a graph must have to be called a periodic function.