How do I convert from a visual to an analytical proof? For example, it is clear to see that a point on a unit circle at an angle ? will be at y=sin? and x=cos? by drawing a right angle triangle inside of it. But what if I don't trust my eyes when I see the triangle? What if I don't know how to define "draw" or what this analytically entails? Why should we even trust something as animalistic as sight to reflect mathematical truth? This is why I prefer analytical proofs but they are overlooked in most textbooks where a visual proof is easier and gives better intuition.