Another way of remembering exact values:
Imagine you have your left arm outstretched in front of you, with your palm facing your face (so you can see the insides of your hand). Now, Imagine you wanted to find
)
. Put down the first finger (your index finger) on your hand and then, count the number of fingers to the left of that (in this case, there is only 1 finger to the left of your index finger. Now, what you next do, is take the number of fingers on the left, square root it, and divide by two.
I.e. For
:
1 finger to the left, so
 = \dfrac{\sqrt{1}}{2} = \dfrac{1}{2})
Now lets say you wanted to find
)
:
There are two fingers to the left (as your middle finger is
), so:
 = \dfrac{\sqrt{2}}{2})
Now, Index = pi/6, Middle = pi/4, ring = pi/3:
If you wanted to find a Cosine instead of a sine, its simple, you just count the number of fingers to the RIGHT of the finger which you wish to find:
i.e. to find
)
:
There is 1 finger to the right of your ring finger, so we have:
 = \dfrac{\sqrt{1}}{2} = \dfrac{1}{2})
Now, whats even better is finding the Tangent of an angle, since we know that:
 = \dfrac{sin(x)}{cos(x)})
Then we can figure out
)
by counting the number of fingers to the left of the specified finger, square rooting it, then dividing it by the square root of the number of fingers to the right of the specified finger.
i.e. to find
)
:
There are two fingers to the left of your middle finger, and two to the right so:
 = \dfrac{\sqrt{2}}{\sqrt{2}} = 1)
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