Trigonometric Functions (A Unit Circle Approach) [Video]


Dave4Math » Precalculus » Trigonometric Functions (A Unit Circle Approach) [Video]

In this introduction to the six trigonometric functions we explain references angles and the unit circle. We also discuss solving right triangles. Many examples are given.

In this video, I am going to introduce the 6 trigonometric functions and discuss the unit circle. By the end of this video you should have a good understanding of what the trigonometric functions are and basic working knowledge of the unit circle.

Hi everyone, welcome back to my channel, I’m Dave. 

In today’s episode, I am going to begin by discussing the Similar Triangle Theorem from geometry. This theorem will help us understand what the trigonometric functions are functions. Then, I will define the six trigonometric functions and work through several examples. As a result, you will see that an important part of working with trigonometric functions are references angles. Next, I talk about the Pythagorean identities and solving right triangles. In doing so, I will explain references angles and work through many examples. I explore other topics as well.

Before getting started you may want to review this video here that discusses angles and their measure.

Now let’s get started.


What are the six basic trigonometric functions?

The six basic functions are the sine, cosine, and tangent functions along with their corresponding reciprocal functions cosecant, secant, and cotangent functions.

What are trigonometric functions used for?

Trigonometric Functions A Unit Circle Approach

The trigonometric functions are the basic building blocks of trigonometry. They allow use to solve triangles and work with angles. These functions also support a functional representation of wave behavior. Many fields of physics use these functions to make an indispensable understanding of the natural world.

How do you find trigonometric functions?

The definitions of the six trigonometric functions are in terms of the sides of a right triangle. Hence given some information about a right triangle we can then find the missing information. In this way, we can solve right triangles. In doing so, we can find the others.

What are the 3 basic trigonometric functions?

The three basic trigonometric functions are sine, cosine, and tangent. The sine and cosine functions are related through the Cofunction Theorem and the other three are the reciprocal functions cosecant, secant, and cotangent functions, respectively.


In this video, I went over what the six trigonometric functions are. You learned how to work with special angles using the unit circle and reference angles. In other words, by solving right triangles and other examples you saw the basic utility of these functions. However, this is just a basic understanding of the trigonometric functions. Indeed, you need much more studying after a basic introduction to fully understand and utilize these important functions. In fact, this video is the second in the Precalculus series. In addition, you should continue on with the next video to gain better understanding of these functions.

Now I wanna turn it over to you. 

Which is your favorite trig function and why? Either way let us know what you think in the comments below right now.

If you like this article or the video, please like or leave a comment and subscribe to my channel.

dave at dave4math

David Smith (Dave) has a B.S. and M.S. in Mathematics and has enjoyed teaching precalculus, calculus, linear algebra, and number theory at both the junior college and university levels for over 20 years. David is the founder and CEO of Dave4Math.