Here is an article that shows that taylor series for sinus becomes very accurate: http://dotancohen.com/eng/taylor-sine.php I wondered if I could prove the sinus values. Explanation for taylor formula have I found here before but the proof for derivative of sinus and cosine relies on values for sinx and cosx which is circular. I might as well upload my attempt to prove cosine to show what I mean. (The same problem goes for sinus): Step1 http://www.viewdocsonline.com/document/4bp3pb Step2 http://www.viewdocsonline.com/document/8e1qd2 Step3 http://www.viewdocsonline.com/document/tx1cp3 Summary http://www.viewdocsonline.com/document/5f54l8 The biggest problem of circularity in the proof that I found was that it uses values for sinA and sinB and cosA and cosB to pytagoras theorem in part one for rewriting identity. Does anyone know a way around this to be able to prove values for sinx?