homechevron_rightProfessionalchevron_rightEngineering

# Trigonometric functions

This online calculator computes the values of elementary trigonometric functions, such as sin, cos, tg, ctg, sec, cosec for an angle, which can be set in degrees, radians, or grads.

Trigonometric functions are the set of elementary functions which relates the angles of triangle to the lengths of the sides of the triangle. They're also called circular functions, see picture.

The trigonometric functions are:
sin — sine
cos — cosine
tg — tangent
ctg — cotangent
sec — secant
cosec — cosecant
versin — versine (versed sine)
vercos — vercosine (versed cosine)
haversin — haversed sine
exsec — exsecant
excsc — excosecant

To compute these functions just enter angle value in Angle field and get the table of results. Angle can be entered in degrees, radians, grads, minutes or seconds.

### Trigonometric functions

Digits after the decimal point: 10
Value of trigonometric functions
Save the calculation to reuse next time, to extension embed in your website or share share with friends.

Well, some school-level theory.

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 expressed via 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)
Secant: $\operatorname{sec}\alpha=\frac{1}{\cos\alpha}$
(the ratio of the length of the hypotenuse to the length of the adjacent side)
Cosecant: $\operatorname{cosec}\alpha=\frac{1}{\sin\alpha}$
(the ratio of the length of the hypotenuse to the length of the opposite side)

Other trigonometric functions:

Versed sine: $\operatorname{versin}\alpha=1 - {\cos\alpha}$

Coversed sine: $\operatorname{coversin}\alpha=1 - {\sin\alpha}$

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

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

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