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## Thursday, August 6, 2009

### Trig Reference Angle Cheat Hand

Observe...

Flip down the finger that corresponds to the angle whose sine and cosine you need.
The number of fingers to the left gives you the sine, and the number of fingers to the right gives you the cosine.

So if you flip down your index finger which corresponds to 30 degrees...
there is one finger to the left.

$sin{(30)}=\frac{\sqrt{1}}{2}$

and there are three fingers to the right.

$cos{(30)}=\frac{\sqrt{3}}{2}$

Try it for the fingers that correspond to the other reference angles. For example, if you flip down your pinky, there are four fingers to the left $sin{(90)} = \frac{\sqrt{4}}{2} = 1$ and zero fingers to the right $cos{(90)} = \frac{\sqrt{0}}{2} = 0$. It works!

It's just another way of organizing the cofunction behavior of sine and cosine to remember the values of five reference angles, but adults and kids both flip out when I show them. Kids especially feel that they "don't have to memorize" if they know this method.