How to Find the Period of a Trig Function

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: How to Find the Phase Shift of a Trig Function

You're on a roll. Keep up the good work!

Take Quiz Watch Next Lesson
Your next lesson will play in 10 seconds
  • 0:00 Steps for Finding the Period
  • 2:40 Solution
  • 3:32 Example
  • 3:58 Lesson Summary
Save Save Save

Want to watch this again later?

Log in or sign up to add this lesson to a Custom Course.

Log in or Sign up

Speed Speed

Recommended Lessons and Courses for You

Lesson Transcript
Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Expert Contributor
Kathryn Boddie

Kathryn earned her Ph.D. in Mathematics from UW-Milwaukee in 2019. She has over 10 years of teaching experience at high school and university level.

Read this lesson to learn how you can find the period of any trig function you are given. You'll see how the period changes when dealing with cosine and sine functions versus tangent and cotangent functions.

Steps for Finding the Period

Did you know that if you are given a trig function and asked to find the period, all you have to do is to look at one particular number and make a simple calculation?

That's right! Looking at this function, you might think you have to do something complicated, but you only need to worry about one of the numbers to figure out your period.

trig period

The period is defined as the length of a function's cycle. Trig functions are cyclical, and when you graph them, you'll see the ups and downs of the graph and you'll see that these ups and downs keep repeating at regular intervals.

trig period

All you have to do is to follow these steps.

Step 1: Rewrite your function in standard form if needed.

The first step you need to take is to make sure that your function is written in standard form:

trig period

The trig word in the function stands for the trig function you have, either sine, cosine, tangent, or cotangent. The A stands for the amplitude of the function, or how high the function gets. The B value is the one you use to calculate your period. When you divide your C by your B (C / B), you get your phase shift. The D stands for any vertical shift the function has. The vertical shift is how much above or below the x-axis the function is shifted.

The trig function from the beginning of this lesson, f(x) = 3 sin(4x + 2), already happens to be in standard form, so you don't have to do anything here.

Step 2: Label your A, B, C, and D values.

After rewriting your function in standard form if needed, now you can label your A, B, C, and D values.

For our example trig function, your A is 3, your B is 4, your C is -2, and your D is 0. Be careful here when it comes to labeling your C value. The C value is negative in the standard form, so if your C value is being added, then your C value is really negative.

Step 3: Calculate your period.

Your next step is to calculate your period using just the B value that you labeled in step two. You'll use two formulas to find your period.

If your trig function is either a sine or a cosine, you'll need to divide two pi by the absolute value of your B.

trig period

To unlock this lesson you must be a Member.
Create your account

Additional Activities

Finding the Period of Secant and Cosecant

In the video lesson, we learned how to find the period of various trigonometric functions. If the trigonometric function is in standard form:

where "trig" is sine, cosine, tangent or cotangent, we learned that the B value is used to find the period. The period for sine or cosine is given by:
And the period for tangent or cotangent is given by:
But what if the trigonometric function is secant or cosecant?

Definition and Graphs of Secant and Cosecant

The cosecant function is defined as one divided by sine and the secant function is defined as one divided by cosine.

The cosecant function has vertical asymptotes where the sine function is zero and the secant function has vertical asymptotes where the cosine function is zero.

Graph of f(x)=csc(x)

Graph of f(x)=sec(x)

Since secant and cosecant are related to sine and cosine, you may think that the period is calculated similarly to the period of sine and cosine - and you'd be right! If the secant or cosecant function is in standard form, the period of the function is given by:


1) Find the period of f(x) = 3sec(2x-5)+3

2) Find the period of g(x) = -2csc(3x+9) - 1

3) Find the period of h(x) = 5sec(-0.5x+1)-12


Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use

Become a member and start learning now.
Become a Member  Back
What teachers are saying about
Try it risk-free for 30 days

Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it risk-free for 30 days!
Create an account