Do you dread having to memorize the values of sine, cosine, and tangent? Are you looking for a clever trick to help you remember these equations without having to constantly refer to a chart? The unit circle hand trick is a great way to quickly recall the angles associated with trig functions, without having to remember the actual values. In this article, we will discuss why and how the unit circle hand trick works, along with some helpful examples, tips, and common mistakes to avoid.

What Is the Unit Circle Hand Trick?

The unit circle hand trick is an unbelievably simple and effective way to remember trigonometric values without consulting a chart. It works by assigning a letter in the alphabet to a certain angle. This allows you to quickly recall the value of the angle simply by looking at your fingers. While this technique is extremely helpful for those studying trigonometry, it can also be used for any angle you need to remember.

How Does the Unit Circle Hand Trick Work?

To use the unit circle hand trick, simply hold up your left or right hand, with your palm facing outward. Using your thumb as the starting point, spell out the alphabet, starting with your pointer finger as A, your middle finger as B, and so on. Now, you can assign each letter of the alphabet with a corresponding angle.

For example, A would be equal to 0 degrees, B equal to 45 degrees, C equal to 90 degrees, and so on. This will continue all the way until you get to Z, representing 330 degrees. Now that you know how to assign angles to letters, all you have to do is remember the letter associated with the angle you need. This technique makes remembering trigonometric functions much easier because it eliminates the need to calculate each angle.

Benefits of Using the Unit Circle Hand Trick

The unit circle hand trick is not only easy to learn but also provides many benefits. One of the greatest advantages is that it is an incredibly quick way to memorize angles. Instead of having to do multiple calculations or referring to a chart, you can simply glance at your fingers and recall the necessary angle in seconds. Additionally, you don’t have memorize numbers; all you have to do is remember letters. This makes the unit circle hand trick easy to remember and simpler to apply.

Examples of How to Use the Unit Circle Hand Trick

Let’s look at some real-world examples of how to use the unit circle hand trick to remember trigonometric functions. To begin, let’s look at the value of cosine across the entire unit circle—starting from 0 degrees and moving in a clockwise direction. To recall the value of cosine from 0-90 degrees, your finger order would be: A-B-C. Now, when looking at cosine from 90-180 degrees, your finger order would be: D-E-F. Once you become familiar with this technique, you will be able to quickly recall all angles and their respective trigonometric values.

Tips for Remembering Trigonometric Values with the Unit Circle Hand Trick

Here are some tips that you can use to help you remember trigonometric values with the unit circle hand trick.

  • Practice makes perfect: The more you practice using the unit circle hand trick, the better you’ll become at remembering angles and their corresponding values.
  • Group similar angles together: It can be helpful to group angles together based on their proximity—such as all angles between 0-90 degrees—to make remembering easier.
  • Use mnemonic devices: It can be helpful to use mnemonic devices when memorizing trigonometric values. For example, for 30 degrees, you can think of it as “halfway between A and B”.
  • Draw it out: Another helpful tactic is to draw out a unit circle on paper or in a math textbook and practice assigning letters and angles by looking at your fingers.

Common Mistakes to Avoid When Using the Unit Circle Hand Trick

Although the unit circle hand trick is an amazing tool for recalling trigonometric values quickly, there are some common mistakes you should avoid in order to make this technique as effective as possible.

  • Forgetting A=0: It’s common for people to forget that A is equal to 0 degrees. This is why it’s important to make sure that A is your starting point every single time.
  • Misrepresenting angles: Make sure that you are assigning the correct angle to each letter. For example, K should represent 90 degrees and not 110 degrees.
  • Not double-checking: Even though this technique makes recalling angles fast and easy, it’s important to double-check yourself and make sure that the letter assigned matches up with the correct angle.

Additional Resources on Trigonometry and the Unit Circle Hand Trick

If you’re looking for more information on trigonometry or helpful techniques for memorizing angles, there are plenty of resources available online. Here are a few websites that offer additional help and information on the unit circle hand trick:

The unit circle hand trick is an easy and convenient way to remember trigonometric values without having to constantly refer to charts. Once you understand how this technique works and practice using it, you’ll find that it’s an immensely useful tool for memorizing angles quickly and accurately.