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Memorize those common ratios!

Some students just don't take the time to memorize the outputs of the trigonometric operations on the more common angles. If you can memorize the values of the trig functions on the angles 0, 30, 45, 60 and 90 degrees (0, pi/6, pi/4, pi/3 pi/2 radians), you will save a ton of time on trigonometry, precalculus, calculus and physics assignments/tests.

Here's a demonstration of a pattern in the values of the sin and cos of these angles that might help you remember these values more easily.

angle | 0 | 30 | 45 | 60 | 90 |
sin | rt(0)/2 | rt(1)/2 | rt(2)/2 | rt(3)/2 | rt(4)/2 |
cos | rt(4)/2 | rt(3)/2 | rt(2)/2 | rt(1)/2 | rt(0)/2 |

where rt(x) is the square root of x.

Notice that the template of sin of these angles is rt(n)/2 with n from 0 to 4 and that cos is also rt(n)/2 with n from 4 to 0. Most of the values simplify, giving the more common display of the values of sin (0, 1/2, rt(2)/2, rt(3)/2 and 1) and cos (1, rt(3)/2, rt(2)/2, 1/2 and 0). This pattern should help you if you're ever blanking on a particular value.

Also, if you need a value of the tan of one of the common angles, remember that tan(x)=sin(x)/cos(x). Just take the quotient of the sin and cos values of that angle!