Wikipedia:Reference desk/Archives/Mathematics/2013 November 24

= November 24 =

Angle sum diagram question
I found the following image to explain the trigonometric angle additive formula. Sadly there is no explanation to go along with it. Could someone try to explain it a little better? - Letsbefiends (talk) 12:27, 24 November 2013 (UTC)


 * The line in bold with the 1 on it is of length 1. It is the hypotenuse of a right angle triangle with angle β which gives the sin β and cos β. The cos β line is the hypotenuse of a right angle triangle with angle α so it has sides sin α and cos α both multiplied by cos β. Same thing with the sin β line.  The original line is also the hypotenuse of a right angle triangle with angle α+β, the opposite side is the sin(α+β) line up from the origin and the adjacent side is the cos(α+β) segment going horizontally from the top left.
 * Overall the diagram can be used to show the sine and cosine of sum identities
 * $$\sin(\alpha + \beta) = \sin \alpha \cos \beta + \cos \alpha \sin \beta$$
 * $$\cos(\alpha + \beta) = \cos \alpha \cos \beta - \sin \alpha \sin \beta$$
 * because the opposite sides of the rectangle are equal. Hope that helps Dmcq (talk) 13:09, 24 November 2013 (UTC)
 * Oh!!! That's a great explanation! Thanks :-) - Letsbefiends (talk) 11:56, 25 November 2013 (UTC)