Wednesday, May 1, 2013

Trig Hand

This is not new. You can read about it here, here, here, and here, just to name a few. 

As of a few months ago, it was new to me. How did I miss this?! I found it when I was searching for unit circle resources, and I thought it was pretty cool. . . Evaluate trig ratios for special angles, quick-and-dirty. I taught my students to use it. That went well.

Here's the summary, followed by the brain dump:

Use your left hand, palm facing you.

Fold over the finger that corresponds to a reference angle. For 45 degrees, there are 2 fingers below and 2 fingers above the bent finger. For 30 degrees, there is one lower finger and three uppers. And so on. Also, I have freakishly small hands. We'll talk about that later.

Then use these three rules:

Other thoughts, in the order they came out of my head:

The trig hand works for angles in other quadrants if you identify the reference angle and know whether the sign should be positive or negative.

It also works if you count the thumb as 90 degrees (four lower fingers and zero upper fingers) and the pinky as 0 degrees (zero lower fingers and four upper fingers), but doesn't extend to the other quadrantal angles. This go-round, I taught these angles separately and used the hand for all four quadrants.

Wait a minute . . . What if the pinky represents the x-axis and the thumb represents the y-axis? Now doesn't the rule also apply to 180 & 270? You would have to add the negative, but we already did that for the other quadrants. Hmmmm.

For finding reference angles my students observed this pattern:
45, 135, 225, and 315 all have 45 degree reference angles and all end in 5.
60, 120, 240, and 300 all have 60 degree reference angles and are all divisible by 60.
30, 150, 210, and 330 all have 30 degree reference angles and are all divisible by JUST 30.
Similar patterns can be found using radians.

My biggest concern, as we all know, is that memorized tricks don't stick. I spent a lot of time on conceptual understanding before I introduced this but still . . .

For next time, I am thinking this is a better fit for my Calculus class. In Algebra 2, students need to understand the why. In calc, we would expect that the understanding is already there. Meanwhile, it would be really convenient to have a quick-and-dirty way to find these values when they pop up.

Finally, someone in almost every class pointed out that, "Mrs. Gruen, I think you have the world's smallest pinky".


Two nickels. They might be right.

1 comment:

  1. Great tip! Agree with you that the handy reference (trying to avoid "trick" and make a great pun at same time) probably works best in calculus.