Trigonometry

Some fundamentals of trigonometry are required for calculus.

Functions

The trigonometric functions relate angles of a right triangle (or the unit circle: r = x² + y²) to the lengths of their sides.

The inverse trigonometric functions are arcsine, arccosine, and arctangent. The name derives from the fact that they are used to relate arc lengths to angles. There are variable notations:

• arcsine of x = arcsin(x) = sin^-1(x)

• arccosine of x = arccos(x) = cos^-1(x)

• arctangent of x = arctan(x) = tan^-1(x)

The hyperbolic trigonometric functions are parallels of these for the unit hyperbola: r = sqrt(x² - y²).

The inverse hyperbolic trigonometric functions are used to relate hyperbolic values back to a hyperbolic angles. There are variable notations. In particular, note that there is disagreement relating to ar- and arc- prefixes. Some notations prefer the latter to parallel the non-hyperbolic functions. On the other hand, as these functions do not relate to actual arcs but rather to area, other notations omit the c.

• inverse hyperbolic sine of x = arsinh(x) = sinh^-1(x)

• inverse hyperbolic cosine of x = arcosh(x) = cosh^-1(x)

• inverse hyperbolic tangent of x = artanh(x) = tanh^-1(x)

• inverse hyperbolic cosecant of x = arcsch(x) = csch^-1(x)

• inverse hyperbolic secant of x = arsech(x) = sech^-1(x)

• inverse hyperbolic cotangent of x = arcoth(x) = coth^-1(x)

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