exact trig values tan mnemonic

How do you remember all the follow tan values:

To remember the values of the key angles for 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.

But now flip your hand upside down with your thumb pointing downwards.

Use the formula:

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

`tan 0° =``(√4)/(√0)``=0`

`tan 30° =``(√1)/(√3)``=(1)/(√3)`

`tan 45° =``(√2)/(√2)``=(1)/(1)``=1`

`tan 60° =``(√3)/(√1)``=√3`

`tan 90° =``(√4)/(√0)``=(√2)/(√0)``= text(undefined)`

Note: If you put √2 divide by 0 in a calculator it will say "undefined."