Table shows values of trigonometric functions of selected angles. Included functions are: sine, cosine, tangens and cotangens. Both deegres and radians angles are presented.

Trigonometric functions#

Angle in radians	Angle in degrees	sin	cos	tan	cot
Show source $0$	Show source $0 ^\circ$	Show source $0$	Show source $1$	Show source $0$	Show source $-$
Show source $\frac{\pi}{12}$	Show source $15 ^\circ$	Show source $\frac{\sqrt{6} - \sqrt{2}}{4}$	Show source $\frac{\sqrt{6} + \sqrt{2}}{4}$	Show source $2 - \sqrt{3}$	Show source $2 + \sqrt{3}$
Show source $\frac{\pi}{10}$	Show source $18 ^\circ$	Show source $\frac{\sqrt{5} - 1}{4}$	Show source $\frac{\sqrt{10 + 2\sqrt{5}}}{4}$	Show source $\frac{\sqrt{25 - 10\sqrt{5}}}{5}$	Show source $\sqrt{5 + 2\sqrt{5}}$
Show source $\frac{\pi}{8}$	Show source $22\frac{1}{2} ^\circ$	Show source $\frac{2 - \sqrt{2}}{2}$	Show source $\frac{2 - \sqrt{2}}{2}$	Show source $\sqrt{2} - 1$	Show source $\sqrt{2} + 1$
Show source $\frac{\pi}{6}$	Show source $30 ^\circ$	Show source $\frac{1}{2}$	Show source $\frac{\sqrt{3}}{2}$	Show source $\frac{\sqrt{3}}{3}$	Show source $\sqrt{3}$
Show source $\frac{\pi}{4}$	Show source $45 ^\circ$	Show source $\frac{\sqrt{2}}{2}$	Show source $\frac{\sqrt{2}}{2}$	Show source $1$	Show source $1$
Show source $\frac{\pi}{3}$	Show source $60 ^\circ$	Show source $\frac{\sqrt{3}}{2}$	Show source $\frac{1}{2}$	Show source $\sqrt{3}$	Show source $\frac{\sqrt{3}}{3}$
Show source $\frac{5}{12} \pi$	Show source $75 ^\circ$	Show source $\frac{\sqrt{6} + \sqrt{2}}{4}$	Show source $\frac{\sqrt{6} - \sqrt{2}}{4}$	Show source $2 + \sqrt{3}$	Show source $2 - \sqrt{3}$
Show source $\frac{\pi}{2}$	Show source $90 ^\circ$	Show source $1$	Show source $0$	Show source $-$	Show source $0$

Some facts#

Trigonometric functions are:
- sine (sinx) - the ratio of the length of the opposite side to the length of the hypotenuse,
  
  $\sin x = \dfrac{opposite}{hypotenuse}$
- cosine (cosx) - the ratio of the length of the adjacent side to the length of the hypotenuse,
  
  $\cos x = \dfrac{adjacent}{hypotenuse}$
- tangens (tanx) - the ratio of the length of the side opposite to the angle to the length of the side adjacent to this angle,
  
  $\tan x = \dfrac{opposite}{adjacent}$
- cotangens (cotx) - the ratio of the length of the side adjacent to the angle to the length of the side that lies opposite this angle,
  
  $\cot x = \dfrac{adjacent}{opposite}$
- secans (secx) - the ratio of the hypotenuse length to the length of the side adjacent to the angle (inverse cosine),
- cosecans (cosecx) - the ratio of the hypotenuse length to the length of the side opposite the angle of the sine.
The values of trigonometric functions for frequently used angles can be found in mathematical tables.
Sometimes we need to find the value of the selected trigonometric function for less typical angles, e.g. a sine of 51 degrees. Then the function's value can be calculated by developing a given function in the so-called Taylor's serie (or more general: power serie).

$\sin x = x - \dfrac{x^3}{3!} + \dfrac{x^5}{5!} - \dfrac{x^7}{7!} + \cdots = \sum_{n=0}^\infty (-1)^n\dfrac{x^{2n+1}}{(2n+1)!}$

$\cos x = 1 - \dfrac{x^2}{2!} + \dfrac{x^4}{4!} - \dfrac{x^6}{6!} + \cdots = \sum_{n=0}^\infty(-1)^n\dfrac{x^{2n}}{(2n)!}$

$\tan x = x + \dfrac{x^3}{3} + \dfrac{2 x^5}{15} + \cdots = \sum^{\infty}_{n=1} \dfrac{B_{2n} (-4)^n (1-4^n)}{(2n)!} x^{2n-1}, \quad |x|<\dfrac{\pi}{2}$

$cot\ x = \dfrac {1}{x} - \dfrac {x}{3} - \dfrac {x^3} {45} - \dfrac {2 x^5} {945} - \cdots = \sum_{n=0}^\infty \dfrac{(-1)^n 2^{2n} B_{2n} x^{2n-1}}{(2n)!}, \quad 0 < |x| < \pi$

$sec\ x = 1 + \dfrac {x^2}{2} + \dfrac {5 x^4} {24} + \dfrac {61 x^6} {720} + \cdots = \sum^{\infty}_{n=0} \dfrac{(-1)^n E_{2n}}{(2n)!} x^{2n}, \quad |x|< \dfrac{\pi}{2}$
The calculation of the function value by expanding into a power series is used by computers or pocket calculators.
ⓘ Hint: If you are interested in trigonometry you can checkout our other calculators:
- reduction formulas - so-called reduction formulas table, that help to calculate value of trigonometric functions for less common angles,
- trigonometric functions values - a table containing the values of trigonometric functions for the most common angles, e.g. sin 90 degrees,
- trigonometric identities - a list of different, more or less popular, dependencies between various trigonometric functions.

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trigonometric_functions · values_of_trigonometric_functions · sine_values · cosine_values · tangens_values · cotangens_valus

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funkcje_trygonometryczne · wartosci_funkcji_trygonometrycznych · wartosci_sinusa · wartosci_kosinusa · wartosci_tangensa · wartosci_cotangensa

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