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

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November 24

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Angle sum diagram question

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Trigonometric angle additive formula

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)[reply]

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
because the opposite sides of the rectangle are equal. Hope that helps Dmcq (talk) 13:09, 24 November 2013 (UTC)[reply]
Oh!!! That's a great explanation! Thanks :-) - Letsbefiends (talk) 11:56, 25 November 2013 (UTC)[reply]