For proofs such as the derivative of cos or sin.. should I study them both analytically and geometrically? By analytically I mean to derive them by algebraic means. Or should I also study the geometrical "intuition" behind it? I love proofs but aren't completely fond of the geometrical "proofs", I was watching MIT opencourseware and stumbled upon the geometrical "proofs" of things like derivatives of cos and sin. Question is, should I even bother to understand them? For a little background: I love mathematics and I'm pursuing theoretical physics. I'm only up to calculus at the moment and I'm trying to understand as much of the proofs as possible; simply because I find it fun and worthwhile. Is it necessary to start developing the geometrical intuition behind some proofs? Would it help for my further studies? As of the moment I see it as a waste of time, and enjoy the "real" proofs much more.