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:

For any sine of an angle, square root the number of fingers BELOW and divide by 2.

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

For any sine of an angle, square root the number of fingers BELOW and divide by 2.

Example: Sin 30°

For any sine of an angle, square root the number of fingers BELOW and divide by 2.

Bend back your 30° finger.

For any sine of an angle, 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°

And count the number of fingers ABOVE.

Bend back your 30° finger.

And count the number of fingers ABOVE.

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

For any tan angle turn your hand upside down and square root fingers above, divided by, square root fingers below.

Example: Tan 30°

For any tan angle turn your hand upside down and square root fingers above, divided by, square root fingers below.

Flip hand and bend your 30° finger.

For any tan angle turn your hand upside down and square root fingers above, divided by, square root fingers 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.