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How to Find the Frequency of a Trig Function

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  • 0:04 Frequency of Trig Functions
  • 0:31 Finding the Frequency
  • 2:21 Other Trigonometric Functions
  • 4:32 Lesson Summary
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Lesson Transcript
Instructor: Gerald Lemay

Gerald has taught engineering, math and science and has a doctorate in electrical engineering.

In this lesson, we explore how to determine the frequency of trigonometric functions. In addition to the sine function, we will look at cosine, tangent, cotangent, cosecant, and secant.

Frequency of Trig Functions

Frequency is a measure of how often something repeats. Trigonometric functions are repetitive. The trigonometric functions we'll look at today include sine, cosine, tangent, cotangent, secant, and cosecant. We'll plot the function and then measure the period, which is the distance between two identical and consecutive portions of a curve. Then we'll take the reciprocal of the period to obtain the frequency.

Finding the Frequency

Let's break down the process of finding the frequency into five simple steps.

Step 1: Plot the function.

For this lesson, we'll assume we already have the plot. For example, the plot of y = sin(πt) looks like this:


The sine function
sine


The green dashed vertical lines are described in the next step.

Step 2: Identify a repeating part of the curve.

For the sine function, we can spot the locations of the maximum portion of the curve. In the plot, the vertical lines locate two consecutive maximums.

Step 3: Measure the period.

The crossing of the vertical line on the horizontal axis tells us a value. The green vertical line crosses the horizontal axis at x = 0.5 and at x = 2.5. The period, T, is the difference between these two values.


period_for_sine


We will assume the units of the horizontal axis are seconds. Thus, T = 2 seconds.

Step 4: Calculate the frequency.

The frequency, f, is the reciprocal of the period. Thus,


frequency_for_sine


The units of frequency are cycles per second, which are also called hertz. Thus, the frequency is 0.5 hertz.

Step 5: Interpret the result.

A frequency of 0.5 hertz is the same as 1/2 hertz. Interpreting this result is a good way to check our understanding and verify we're consistent with the graph.

1/2 hertz indicates one cycle every two seconds. And this is exactly what we see on the graph.

Other Trigonometric Functions

We can use the same method to determine the frequency of other trig functions. Let's work through a few examples.

First, we'll look at the cosine function. The cosine function is a shifted version of the sine function.


Finding the frequency of the cosine function
cosine


The minimums were chosen as the identifiable feature here, but any easily recognizable feature will work. The period is the difference between 3 seconds and 1 second. Thus, T = 3 - 1 = 2 seconds. The frequency is 1/T. Thus, f = 1/2 hertz.

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