sine of angle of triangle

The cosines law allows to express the cosine of an angle of triangle through the sides:

cosα=b2+c2-a22bc. (1)

Substituting this to the “fundamental formula of trigonometryMathworldPlanetmath”,

sin2α+cos2α= 1,

we can calculate as follows:

sinα =+1-(b2+c2-a22bc)2

Thus we have the beautiful formula


Substituting (1) similarly to the general formula for the sine of half-angle (


one can obtain the formula

Title sine of angle of triangle
Canonical name SineOfAngleOfTriangle
Date of creation 2013-03-22 18:27:16
Last modified on 2013-03-22 18:27:16
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 5
Author pahio (2872)
Entry type Derivation
Classification msc 51M04
Related topic DifferenceOfSquares