Remember exact trig values mnemonic summary

How do you remember all the following values?

To remember the values of the key angles for for sin, cos and tan, use the following mnemonic or hand trick. 

First assign all the fingers on one hand using zero to ninety with the thumb sticking up, as follows:

Your thumb = 90°
Index finger = 60°
Middle finger = 45°
Ring finger = 30°
Pinky finger = 0°

Example: Sin 30°

For any sine of an angle bend back the appropriate finger and square root the number of fingers BELOW and divide by 2.

And count the number of fingers BELOW.

`sin = \sqrt{1 \text( finger) \text( BELOW)}/2 = \sqrt{1}/2 = 1/2`

Example: Cos 30°

For any cos of an angle bend back the appropriate finger and square root the number of fingers ABOVE and divide by 2.

Bend back your 30° finger.

And count the number of fingers ABOVE.

`cos = \sqrt{3 \text( fingers) \text( ABOVE)}/2 = \sqrt{3}/2`

Example: Tan 30°

For any tan of an angle bend back the appropriate finger, turn your hand upside down and square the number of fingers above, divided by, the square root of the numbers of fingers below.

Turn you hand upside down.

And count the number of fingers above AND below.

`tan 30 = \sqrt(\text(number of fingers ABOVE))/\sqrt(\text(number of fingers BELOW)) = \sqrt(1)/\sqrt(3) = \(1)/\sqrt(3)`

Summary

For all the exact trig values using a hand trick or mnemonic see the following pages.