What are the trigonometric functions and ratios?

Answer 1

In all there are [at least] 24 trigonometric functions and ratios. Half of these are circular and the other half are hyperbolic.

Sine and Cosine are basic trigonometric funtions, abbreviated as sin and cos.

Tangent is the third basic ratio defined as Sin/Cos.

For each of these three, there is a corresponding reciprocal function:

Sine -> Cosecant (cosec or csc)

Cosine -> Secant (sec)

Tangent -> Cotangent (cot).

Each of the above six has an inverse function, defined on an appropriate domain. They all are named by adding the prefix "arc", for example arcsin, which is usually written as sin-1.

The above are the circular functions. Each one of them has a corresponding hyperbolic equivalent. These are named by adding the suffix, "h", thus cosh, sech, arccosh [= cosh-1], etc.