There is a more simple way to remember sin and cos functions of special angles using your hand.

As you can see in the picture we can assign a finger for a special angle. Using your left hand facing towards you, assign the thumb as 0 degrees, the index as 30, the middle finger as 45, the ring finger as 60 and the pinky as 90 degrees.

Now that you have assigned an angle to each finger, you can now solve for sin and cos for angles 0, 30, 45, 60, and 90 by following these steps:

We start of with SIN…

You fold down the finger corresponding to the angle and all the fingers on the right of the angle you are looking for. an example of this would be if you were to look for sin 60, you should fold your ring finger and your pinky finger.

Then the number of fingers that are NOT FOLDED will be inside a square root to become your numerator while 2 will always be the denominator. Lets go back to sin 60, since you have folded your ring finger and your pinky finger then you would have 3 fingers NOT FOLDED so the sin of 60 would be the square root of 3 all over 2.

THIS WILL WORK FOR THE SIN OF THE SPECIAL ANGLES MENTIONED ABOVE.

We now go to COS…

Now in getting the cosine of the angle you now fold down the finger that corresponds to the angle and the fingers left of the finger that corresponds to your angle. for example cos 60, you should fold your ring finger, middle finger, index finger and your thumb.

You will now use the same concept as the one in SIN so, the number of fingers that are NOT FOLDED would be inside a square root which serves as your numerator, and 2 will still be your denominator. For this example since you only have 1 as your numerator and the square root of 1 is also 1 so cos 60 would then be equal to 1/2.

To get the tangent simply divide sine by cosine.