I’d like to think that the following constitutes a Proof without Words of the formulas for the derivatives of sine and cosine.
Unfortunately, it seems that words may be in order, so I wrote some here: “Calculus-free Derivatives of Sine and Cosine” … even though, strictly speaking, the proof isn’t entirely calculus-free. (Why we expect the projection of the tangent line to a helix to be tangent to the planar projections of the helix needs justification.)
But the idea is good for the intuition.
I even made an interactive illustration for the Wolfram Demonstrations Project.