IMPORTANT! This activity is a SUPPLEMENT to your lesson on the Unit Circle. Your students must know how to create it using Special Right Triangles. This activity is meant to create a recall point for your students. Meaning, something exciting to remember the lesson by and its importance. So when they hear the terms Unit Circle they think back and go “Oh Yeah! That is the day we did the hand trick.”
With that said this unit circle activity is also good as a last resort for those students who just cannot grasp the creation of the unit circle. What I have noticed my advanced students love it too because once they have learned this little trick they can quickly use it to recall the piece of the circle they need. These students can also very quickly figure it out using the special right triangles or by memorizing the first quadrant. For me I just like it as an activity that the students can remember the lesson by. It is out of the ordinary and a change of pace from normal math activities.
With that said. Here is the lesson…
Unit Circle Hand Trick
You will want your students to use the hand opposite the one that they write with. If they write with their right hand use their left, if they write with their left hand then use their right. The reason for this is so they can write while looking at their other hand to remember the ‘trick’. The below pictures shows how to hold your hands.
Each one of your five fingers represents a special point on the Unit Circle:
Thumb – 0° or 0π (2π)
Index Finger – 30° or π/6
Middle Finger – 45° or π/4
Ring Finger – 60° or π/3
Pinky Finger – 90° or π/2
Finding Sine and Cosine: First Quadrant
When finding sine and cosine remember your answer always looks like the square root of something over two (√?/2).
Step One:
To find the value for sine/cosine just fold down the respective finger. For example, if we wanted to find sine/cosine values for 30° or π/6 we would fold down the index finger.
Step Two:
Now we turn our hands into an ordered pair; parentheses on the outside and a comma where the folded down finger is.
So continuing with our example of 30° or π/6 we get (3,1).
Step Three:
We must now implement what was stated before step one (√?/2), which gives us (√3/2, √1/). This simplifies to (√3/2, 1/2).
Step Four:
Since we know on the unit circle, the ordered pairs are presented (cosine, sine) we can conclude that the sin(30°) or sin(π/6) is equal to 1/2 and the cos(30°) or cos(π/6) is equal to √3/2.
Note: This does work for 0° and 90°. 0/2=0 and √4/2=2/2=1.
Finding Sine and Cosine: Second Quadrant
This is almost as easy as the process for Quadrant I, but with a few small changes. First things, first, we need to flip our hands (just like a reflection over the yaxis). Now each finger represents a new point on the unit circle:
Pinky Finger: 90° or π/2
Ring Finger: 120° or 2π/3
Middle Finger: 135° or 3π/4
Index Finger: 150° or 5π/6
Thumb: 180° or π
Now we follow steps one through three for Finding Sine and Cosine: First Quadrant.
For example, if we were trying to find the sine/cosine values of 120° or 2π/3 we would get (√3/2, 1/2).
Step Four:
Since we flipped our hands over the yaxis, we now must switch our values in our ordered pair.
Thus we now have (1/2, √3/2).
Step Five:
Finally we must apply negative signs where appropriate for the second quadrant (the xvalue of the order pair).
Therefore we end up with (1/2, √3/2) and can conclude that sin(120°) or sin(2π/3) is equal to 1/2 and cos(120°) or cos(2π/3) is equal to √3/2.
Finding Sine and Cosine: Third Quadrant
This is exactly the same as Finding Sine and Cosine: Second Quadrant, except for step five, we now negate both value of the ordered pair. (You also have to reflective your hand again, this time over the xaxis. Or starting from the original position, rotate 180° counter clockwise. This is an awkward position for the right handed people. Fingers will also now represent new positions on the unit circle.)
Finding Sine and Cosine: Fourth Quadrant
Starting from the original position, flip your hand down (reflect over the xaxis). Fingers will also now represent new positions on the unit circle. (This is an awkward position for the left handed people)
Follow steps one through three for Finding Sine and Cosine: First Quadrant.
Step Four:
Apply negative signs where appropriate for the fourth quadrant (the yvalue of the order pair).
Finding Tangent:
Follow step one and two for Finding Sine and Cosine: First Quadrant. Going back to our example of 30° or π/6 we get (3,1).
Step Three:
Rotate your ordered pair 90° counter clockwise and turn into a fraction.
Step Four:
Place fraction under radical sign and simplify.
Step Five:
If you use this in your classroom, please leave a comment below; I am curious as to how your students will react.
This is a blog post I came across on Pinterest. I wanted to share it with everyone! Absolutely amazing idea! I tried to reach out to Ms. Smith, the creator of the lesson, to interview her but there doesn’t seem to be a contact form on her page. If anyone knows how to get a hold of her please let us know. Amazing Idea! Her blog post can be found at http://highschoolmathadventures.blogspot.com/2013/08/UnitCircleHandTrick.html
If you are looking for more amazing Geometry Lessons be sure to subscribe to our email list. We will also send you all of our worksheets, tests, quizzes, lesson plans, videos, slide shows, and everything else you would need to teach the first Unit of Geometry absolutely FREE! Simply Click Here or the image below.

Find and Use Slopes of Lines

Teaching Midpoint and Distance in the Coordinate Plane

Teaching Congruent Figures

Triangle Congruence by ASA and AAS

Teaching Perpendicular and Angle Bisectors

Teaching Bisectors in Triangles

Best Geometry Books for Kids

Proving Theorems in Geometry

How to Prove Lines Are Parallel

Teaching Logic in Geometry

Teaching Angle Pairs

Proofs with Uno Cards

Valentine’s Day Math Activity – Classifying Quadrilaterals

Christmas Math Worksheets

Thanksgiving Worksheet for Geometry – Happy Turkey Day!

Halloween Geometry Activities High School

How to Teach Classifying Polygons

Points Lines and Planes

Tessellation Project

Introduction to Trigonometry

Pi Day Top 5 for Geometry Teachers

Polygons in the Coordinate Plane – How to use Geogebra

Teaching Tessellations to Your Geometry Class

3 Ways to Make Your Life Easier as a Geometry Teacher Without More Geometry Worksheets

Reasoning and Proof

Geometry Games – Dance Dance Transversal

Midsegments of Triangles

Planning a Proof

Triangle Congruence by SSS and SAS

Pythagorean Theorem – NFL and Geometry

Inequalities in One Triangle

Parallel Lines Cut by a Transversal – Colorful Flip Book Notes

Measuring Angles PuttPutt Course Design Project

How to Teach Tangent Lines – Graphic Organizer

Segment Addition Postulate

Two Tips to Teach Volumes of Prisms and Cylinders

Parallel Lines and Transversals

Nets and Drawings for Visualizing Geometry – Geometry Nets Project

Ratios and Proportions – Bad Teacher!

Hybrid Flipped Classroom Model

How to Teach Perimeter and Area of Similar Figures – in Jay Leno’s Garage

How to Create a Jeopardy Game

5 Tips for New Teachers

8 Teacher Discounts you don’t want to miss this Summer

Your Students are Cheating with this Math App

How to Setup and Use Google Classroom and Google Forms to Teach Geometry

Special Right Triangles – The Foundation of Everything Trig

How to use Google Forms and Word Clouds to Help your Students Master their Geometry Vocabulary

Interactive Geometry Teaching Techniques

The Magic Octagon – Understand Congruence in Terms of Rigid Motions

Attention Getters to Keep Your Geometry Class Locked in!

Teaching Strategies for your Inclusion Geometry Class without an Intervention Specialist

How to Teach the Properties of Quadrilaterals

How to make Geometry Interesting

How to Teach Circles Using the Common Core Standards?

Full Year of Geometry Lesson Plans

How a Rock Star Geometry Teacher Uses the iPad to Educate

Are you a Geometry Teacher with No Textbooks or Geometry Worksheets?

How to Deal with a Class Clown – Classroom Management Strategies

Geometry Lessons  The Game Has Changed  Common Core Standards

Teaching Dimensions with Super Mario – Geometry

Lesson for the First Day of Geometry Class