The Trigonometric Functions
There are two common approaches to the study of trigonometry. In one, the trigonometric functions are defined as ratios of two sides of a right triangle. In the other, these functions are defined in terms of a point on the terminal side of an angle in standard position. We define the six trigonometric functions, sine, cosine, tangent, cotangent, secant, and cosecant (abbreviated as sin, cos, etc.), from both viewpoints.
Definition of the Six Trigonometric Functions
Right triangle definitions, where (see the figure below)
Circular function defiinitions, where θ is any angle (see the figure below).
The following trigonometric identities are direct consequences of the definitions ( is the Greek letter phi).
Trigonometric Identities (Note that sin2θ is used to represent (sin θ)2.)