# 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.

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#### Michele

Created: 2010-03-28 11:46:44, Last updated: 2020-11-09 16:07:37

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Trigonometric functions are the set of elementary functions that relates the angles of a 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, enter the angle value in the Angle field and get the table of results. The angle can be entered in degrees, radians, grads, minutes, or seconds.

#### Trigonometric functions

Digits after the decimal point: 10
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Well, some school-level theory.

Sine of an angle ( sin ) is the ratio of the opposite side's length to the hypotenuse's length.

Cosine of an angle (cos) is the ratio of the adjacent side's length to the hypotenuse's length.

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

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