Rise and Sine

# Fresh Ideas to Teach the Unit Circle in Trigonometry

## It’s Time To Learn The Unit Circle!

I really had to pump myself up to teach my students the unit circle in trigonometry *cue Rocky theme song music*.

I love teaching trig! But the unit circle is a big beast.

Over the years, I created a few ways to help my students not just memorize, but also understand and master the unit circle.

## The Unit Circle Explained

I never want my students to feel like I am trying to trick them. So I almost always teach new topics with guided notes. That way they always have the tools they need to reference when they try to answer their own questions. (It also makes taking notes faster, reduces errors in copying from board to paper, and absent students know exactly what they missed. All teacher wins!)

I usually reserved two class periods to work through my planned Unit Circle guided notes. I’d start with the quadrant angles and find all six trig functions. Then, we would work through the six trig functions of the Special Right Triangles.  First 45˚, then 60˚. Then fill in the answers to the remaining 30˚ triangles.

In the end, we were looking at a whole crazy big long table full of solutions that all looked the same.

Usually, it resulted in a bunch of looks like uh, WHAT?!

But Special Right Triangles are the key to understanding the Unit Circle. And this information is crucial!

In subsequent lessons, we break down that table into smaller parts that are easier to remember and students can breathe a sigh of relief.

Students start to see patterns in the answers, and in the signs of those answers. We would revisit this often.

## Don’t Just Try Memorizing the Unit Circle

The Unit Circle in trigonometry sticks around a while, and so having a strong understanding is important.

I would emphasize the value of knowing the Unit Circle but no matter what – the reference sheet students were supposed to keep in their binders would go missing regularly. (Teenagers, amirite?)

So I adapted! This interactive Unit Circle stands out, clips in their math binder, and is a great hands-on tool!

Students love to engage with the rotating special right triangles and it really emphasizes all the important information contained in the Unit Circle:

• Equivalent angles in degrees and radians, easy to see.
• Quadrants and x/y axis shown to make signs easy to determine
• Special triangles and the values of sine and cosine available to figure out coordinates, or use to determine the other trig functions

Plus it takes effort to put together and seemed to be valued by students more than just a worksheet.

## Fill in the Unit Circle, Digitally!

Save paper, go digital!

The unit circle can be completed on any device using this activity, designed for Google Slides. Students will drag and drop the angles in degrees, angles in radians, and the coordinates to their appropriate places around the circle. There’s also a worksheet included that asks students to find the coordinates of the angle that intercepts the unit circle.

Practice makes perfect! This worksheet can be used again and again. And it might seem a bit less boring than writing it out on paper. Also a great activity to leave with a substitute.

## Provide a Permanent Unit Circle Visual

Students will understand they can’t escape the Unit Circle in trigonometry if it’s constantly displayed for them!

Check out this Unit Circle visual!

Make it a permanent fixture as a bulletin board, or use tape on the angles and coordinates to make students place each piece in the appropriate spot.

Need to differentiate? Start with what you need. Use only degrees (or radians) and leave the extra information off.

## Show Students the Hand Trick

Sure, there’s no substitute for true understanding, but I’m a huge math nerd, and understanding the ins and outs of math is a passion of mine.

Another passion I have is teaching math and showing students they are capable of success even if they don’t consider themselves gifted in math.

So I don’t discredit little tricks like this one if it helps even one student feel more confident when working on the Unit Circle in class.

I eventually learned that not all students are going to grasp material the first way something is taught. Maybe not the second way, and probably not your preferred way.

Who said you can’t count on your fingers, anyway?!

## Printable Unit Circle

Simple and self-explanatory! Students can complete the unit circle in degrees and radians. Available in color to accent angle “families”. Just complete the quick form below and I’ll send this Unit Circle worksheet right to your inbox!

I hope you found some of these lesson options useful to implement in your trig class!

##### Tara

All posts

• […] out my previous post: Fresh Ideas to Teach the Unit Circle in Trigonometry. I share some more ideas on how to incorporate the unit circle into your […]

• […] Not exactly what you’re looking for? Check out my previous post Fresh Ideas to Teach the Unit Circle In Trigonometry. […]

• October 7, 2022 at 9:21 am

[…] Fresh Ideas to Teach the Unit Circle in Trigonometry […]

• March 14, 2023 at 12:04 pm

Thank you for all the information!

• August 12, 2023 at 7:17 pm

Thanks so much!! This will really help me teach the unit circle