Hand-y way to remember Unit Circle exact values

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Confused, much?

Confused, much?

I was recently working with a Year 10 Mathematical Methods student, in preparation for the upcoming exams. She couldn’t remember the exact values of the Unit Circle angles, so I showed her a handy method of remembering. She was impressed (aw, shucks!), so I thought I’d share it here!

Step 1:

Label the thumb of your left hand “SINE”, your index finger “30”, your middle finger “45”, your ring finger “60” and your pinky “COS”. Draw a vinculum with the number 2 as the denominator on your palm. Or, draw divided by 2 on your palm – whichever works! πŸ™‚

See below:

Marked Hand


Step 2:

Step 2 requires some imagination. I want you to imagine that there is a magic square root symbol floating in the air above your fingertips. Can you see it?

Magic Root


Step 3:

If you would like to know what the exact value of, say, Sine 30 degrees, fold down the finger with “30” on it. Like this:


The Magic Root symbol goes over the digit left standing on the Sine side of the hand – in this case the thumb. The root of one (or just one), divided by two – the exact value of Sine 30 is one-half!

Can you also see how the Cosine of 30 can be found?

Below I have lowered the “45” digit – the Sine and Cosine of 45 both equal to root two divided by two! It’s magic!




This little memory trick has worked wonders for Β me over the past few years, particularly with students who have found surds and fractions to be a frightening mix. I have taught this to students in Year 10, who have found it an invaluable tool in their understanding of the Unit Circle.


Here’s a challenge for you or your students. How can we include the exact values for the Tangent into this? πŸ™‚


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