Trigonometry on the Unit Circle
The unit circle
To help us understand the geometric meaning of the trigonometric functions, it is helpful to consider what
CAST rule
The CAST rule is used to help you remember the quadrants in which
Quadrant 1 is represented by A therefore all three are positive in that quadrant.
Quadrant 2 is represented by S therefore
Quadrant 3 is represented by T therefore
Quadrant 4 is represented by C therefore
SOH CAH TOA and special angles
In trigonometry there are special angles at which you should know the value of the various trigonometric functions. The two special triangles below can be used to help you find these values, but first we need to remember how sine and cosine are defined based on the sides of a right angle triangle. To help us remember we use:
Using the above triangles and SOHCAHTOA, we end up with the following chart (note that the angles in the chart below are given in units of radians):
Undefined |
These values can be used to find the values for
Example: Evaluate
Solution: First of all,
Example: Evaluate
Solution: First, we know,
Example one:
Example two: