This article was reviewed by Joseph Meyer and by wikiHow staff writer, Sophie Burkholder, BA. Joseph Meyer is a High School Math Teacher based in Pittsburgh, Pennsylvania. He is an educator at City Charter High School, where he has been teaching for over 7 years. Joseph is also the founder of Sandbox Math, an online learning community dedicated to helping students succeed in Algebra. His site is set apart by its focus on fostering genuine comprehension through step-by-step understanding (instead of just getting the correct final answer), enabling learners to identify and overcome misunderstandings and confidently take on any test they face. He received his MA in Physics from Case Western Reserve University and his BA in Physics from Baldwin Wallace University.
This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources.
This article has been viewed 15,738 times.
Finding the period of a trigonometric function is an essential piece of the pre-calculus puzzle—so how do you do it? The period of a function is the distance between each repeating interval on a graph, or the distance between the peaks of each wave. To learn how to calculate the period of any function, follow the equations and examples below and ace your next math test!
Finding the Period of a Sinusoidal Function
Periodic functions are functions that repeat continuously, and a period is the distance between each repetition. Find the period for a sine function and a cosine function with the formula .
Steps
Finding the Period of a Sine or Cosine Function
-
Find the coefficient B in your sine or cosine function. Your function should follow this function formula: or . Identify the value of B in your formula.[1]
- None of the other coefficients will affect the period of the sine wave, so you can disregard them for now.
-
Plug B into the formula . This formula is used for both sine and cosine functions, so you can follow the same steps for either. Divide by the absolute value of your coefficient B. The absolute value of B is the non-negative value of B. For example, the absolute value is 3 if B equals 3 or -3.[2]
- Suppose your sine function is . In this case, .
- Plug 2 into the formula to get .
- In this case, the period of the sine function is .
- The same steps are used to find the period of a secant function and a cosecant function .
Advertisement -
If your sine or cosine function is or , the period is always . is the period for a standard sine or cosine curve. If no other coefficients or variables are introduced to change the period, the period of or will always be .[3]
Finding the Period of a Tangent Function
-
Find coefficient B in tangent function . If your tangent function is , then Ignore any other whole numbers in the tangent function; i.e. if the function is , you only need to pay attention to 3, which represents coefficient B.[4]
-
Substitute the value of B into the formula . Divide by the absolute value of B to find the period of the tangent function. For example, suppose your tangent function is .[5]
- Plug B (2) into the formula to obtain .
- The absolute value of 2 is 2, which leads us to .
- Solve the equation to get .
- The period of this tangent function is .
- The same steps are used to find the period of a cotangent function .
-
If the tangent function is , the period is always . A standard tangent function will always have a period of . Therefore, you don’t have to calculate the period for function .[6]
Expert Q&A
Video
Tips
-
There are two ways to be sure of the periodicity of a function: if its range repeats itself at regular intervals, and if the function is in the formThanks
References
- ↑ https://flexbooks.ck12.org/cbook/ck-12-algebra-ii-with-trigonometry-concepts/section/14.4/primary/lesson/changes-in-the-period-of-a-sine-and-cosine-function-alg-ii/
- ↑ https://flexbooks.ck12.org/cbook/ck-12-algebra-ii-with-trigonometry-concepts/section/14.4/primary/lesson/changes-in-the-period-of-a-sine-and-cosine-function-alg-ii/
- ↑ https://flexbooks.ck12.org/cbook/ck-12-algebra-ii-with-trigonometry-concepts/section/14.4/primary/lesson/changes-in-the-period-of-a-sine-and-cosine-function-alg-ii/
- ↑ https://www.cuemath.com/trigonometry/tangent-function/
- ↑ https://www.cuemath.com/trigonometry/tangent-function/
- ↑ https://www.cuemath.com/trigonometry/tangent-function/
- ↑ https://www.cuemath.com/algebra/periodic-function/#slide-896
- ↑ https://www.geeksforgeeks.org/periodic-formulas-with-examples/
- ↑ https://americanboard.org/Subjects/mathematics/amplitude-frequency-period-and-phase-shift/