# To Accumulate a Rate — Integrate!

Teaching High School Mathematics

# Trig ratios at your fingertips

I saw a pic on Twitter today that reminded me of a nice way to use your fingers to help memorize the trig ratios. I’m not a crazy huge fan of it because I like to reinvent them using special right triangles. That is if I happen to forget which values go with which trig ratios. However, there is a time and a place (if it’s not sinking in or I know how to get them and now just want to have them at my fingertips) for a good memorization technique.

Here is the pic:

To use your fingers to keep track of all these numbers look at the pictures below. You hold your hand toward you and bend a finger corresponding to the angle you want the trig ratio of. Then…

For cosine take the square root of the number of fingers above your bent finger and then divide by 2 and for sine take the square root of the number of fingers below your bent finger and then divide by 2.

Here’s how to use your fingers for 0 degrees:

Here’s how to use your fingers for 30 degrees:

Here’s how to use your fingers for 45 degrees:

Here’s how to use your fingers for 60 degrees:

Here’s how to use your fingers for 90 degrees:

I didn’t come up with this and I’d love to give credit, but a student showed it to me one time so I guess it’s just out there.