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.

Then one of these functions is 'squared', as in sec²(x), this should be read as multiplying the function's output by itself. In other words, sec²(x) = sec(x) * sec(x).

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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