Trig Double Angle Formulas from Semicircle (visual proof)
This is a short, animated visual proof of the Double angle identities for sine and cosine. To get the formulas we use a semicircle diagram and rely on similarity of two right triangles formed inside.
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For another visual proof of this fact using the laws of sines and cosines, check out this animation:
• A proof to remember: Double Angle For...
This animation is based on a visual proof by Roger B. Nelsen from the January 1989 issue of The College Mathematics Journal (https://www.jstor.org/stable/2686819 - page 51).
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