Fun with the Unit Circle

The Unit Circle

To use the triangles you have to first know the unit circle. The unit circle is divided up in degrees of 30, 45, 60, and 90. They can also be in radians (which are seen on left) respectively. The unit circle itself with both radians and degrees is below. When using the unit circle you can also get negative angles, to find them you simply go around the circle clockwise starting at the 0 degree line. When doing this it is easiest to pretend that the circle is reversed to find the angle and then put it back the original way to find the answer. The easiest way to learn the unit circle is to memorize the first quadrant, the rest of the angles will come easy after that.


Other important information.

In the unit circle some answers will be negative depending on which quadrant of the unit circle they fall in. The quadrants are one through four going around the circle counter-clockwise. All functions in the first quadrant are positive, in the second sin and csc are positive, in the third tan and cot are positive and in the last cos and sec are positive this can be remembered using the phrase All Students Take Calculus (ASTC). Also for 90 degrees, 180 degrees, 270 degrees and 360 degrees you use them as you would a graph with x and y values using only 1's and 0's. The y value is the same as sin and the x is the same as cos. To find the others you use the formals replacing opposite with y and adjacent with x and hypotenuse with 1.