## Social Question # What do you think of this proof of trigonometric angle addition formula?

Asked by LostInParadise (28580 ) May 6th, 2011

I am surely not the first to think of this, but this proof seems more intuitve and straightforward than the usual proofs I have seen using similar triangles. Angle Addition proof I give the proof for the cosine formula. The same diagram can be used for the sine formula.

Observing members: 0 Composing members: 0  Seems intuitive enough, but the first statement, that vector addition is independent of the coordinate frame, seems like a conclusion that might have been reached with the help of trigonometric angle addition. If so, this reasoning is circular. Nevertheless, it would be a good teaching method if not.

In short, did they use preexisting trigonometric angle addition in the background of this proof?

jasonwiese55 (620 )“Great Answer” (1 ) Flag as…  Vector addition uses parallelogram completion. It does not require a coordinate system.

LostInParadise (28580 )“Great Answer” (0 ) Flag as…  @LostInParadise Then it seems good to me.

jasonwiese55 (620 )“Great Answer” (0 ) Flag as…  Its a nice proof, but very hard to follow in its current form.

roundsquare (5517 )“Great Answer” (0 ) Flag as… 