How to Find the Period of a Trig Function

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
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