# How calculators calculate inverse trigonometric functions

## Trigonometric functions

Trigonometric functions are elementary functions that calculate the angles of triangles based on the lengths of the sides of triangles. They are also called circular functions (see picture).

The trigonometric functions are:
sin - Sine
cos - cosine
daily - tangent
ctg - cotangent
sec - secans
cosec - cosecans
versin - sine versus
vercos - cosine versus
haversin - Semiversus
exsec - Exsecans
excsc - Excosecans

To calculate these functions, just put the angle value into that angle Field and you will get a table of results. Angles can be entered in degrees, radians, gradients, minutes, or seconds.

Here are some theories from school:
Sine of an angle (sin) is the ratio of the length of the opposite side to the length of the hypotenuse.

cosine of an angle (cos) is the ratio of the length of the adjacent side to the length of the hypotenuse.

All other functions are represented using the sine and cosine as follows:

Tangent: $\operatorname{tg}\alpha=\frac{\sin\alpha}{\cos\alpha}$
(the ratio of the length of the opposite side to the length of the adjacent side)
Cotangent: $\operatorname{ctg}\alpha=\frac{\cos\alpha}{\sin\alpha}$
(the ratio of the length of the adjacent side to the length of the opposite side)
Secans: $\operatorname{sec}\alpha=\frac{1}{\cos\alpha}$
(the ratio of the hypotenuse to the length of the adjacent side)
Cosecant: $\operatorname{cosec}\alpha=\frac{1}{\sin\alpha}$
(the ratio of the hypotenuse to the length of the opposite side)

Other trigonometric functions:

Sine versus: $\operatorname{versin}\alpha=1 - {\cos\alpha}$

Cosine Versus: $\operatorname{coversin}\alpha=1 - {\sin\alpha}$

Semiversus: $\operatorname{haversin}\alpha=\frac{\operatorname{versin}\alpha}{2}$

Exsekans: $\operatorname{exsec}\alpha=\operatorname{sec}\alpha -1$

Excosecans: $\operatorname{excsc}\alpha=\operatorname{cosec}\alpha -1$