Trigonometric function (thing)

The trigonometric functions (also referred to as the Circular Functions) comprising trigonometry:

• sin - "sine"
• cos - "cosine"
• tan - "tangent"
• sec - "secant"
• csc - "cosecant"
• cot - "cotangent"

Each function has significance in relation to side ratios of right angled triangles. The definitions of each can be found at the corresponding nodes.

The inverses of these functions are denoted:

• sin^-1
• cos^-1
• tan^-1
• sec^-1
• csc^-1
• cot^-1

NB: The f^-1 notation here implies inverse function, as opposed to f raised to the power of -1.

As the function of an angle will give you a ratio of side lengths, so the inverse function of side ratios will give you the angle.

The trigonometric functions are defined in terms of e, in the following way:

         eix - e-ix
sin(x) = ----------
             2i

         eix + -ix
cos(x) = ----------
              2

         eix - e-ix
tan(x) = ------------
         i(eix + e-ix)

             2
sec(x) = ----------
         eix + e-ix

             2i
csc(x) = ----------
         eix + e-ix

         i(eix + e-ix)
cot(x) = ------------
         eix - e-ix

Trigonometric functions are readily manipulated using Trigonometric Identities (Including, but not limited to, Half Angle Formulae and Double Angle Formulae.)

Closely related are the Hyperbolic Functions