- See also Trigonometry/Polar for an approach that is useful for -∞<θ<∞
Fundamental trigonometry functions
There are six trigonometric functions in Trigonometry: sine, cosine, tangent, cotangent, secant, and cosecant.
- Sine θ is the length of the leg opposite θ over the length of the hypotenuse:
- Cosine θ is the length of the leg adjacent to θ over the hypotenuse:
- Tangent of θ is the length of the leg on the opposite side of the triangle from the angle θ over the length of the leg of the triangle adjacent to the angle θ:
These three can be memorized by use of the name of the princess "Soh Cah Toa," meaning:
The remaining ratios are reciprocals of the previous ratios:
- Cotangent θ is the reciprocal of tangent θ:
- Secant θ is the reciprocal of cosine θ:
- Cosecant θ is the reciprocal of sine θ:
- Since the hypotenuse of a right triangle is always the longest side, and
- If we divide both sides of each of these inequalities by the positive number , we get and
- See Table of functions.
- Reading: w:Trigonometric_Functions (Wikipedia)