Precalculus with Unit-Circle Trigonometry

[harpazo]

I suppose that one could learn calculus simply by knowing algebra and arithmetic, but that would be insanely difficult and would not at all track the way the subject developed. Within 50 years of Descartes's work, calculus was in full development.

How did people long ago learn calculus before precalculus became a course?

 

[JeffM]

Actually, I suppose I am responding to the fragment quoted. Based solely on what you quoted, I believe it is technically wrong, but practically obvious. The whole point about analytic geometry is that you can go from elementary algebra to Euclidean geometry or Euclidean geometry to elementary algebra; they are homomorphic so you do not need both. But in terms of learning and exploring, sometimes one gives insight and sometimes the other does so. I believe it is a historical fact that the development of modern algebraic notation and analytic geometry immediately preceded the development of the infinitesimal calculus.

 

[harpazo]

Actually, I suppose I am responding to the fragment quoted. Based solely on what you quoted, I believe it is technically wrong, but practically obvious. The whole point about analytic geometry is that you can go from elementary algebra to Euclidean geometry or Euclidean geometry to elementary algebra; they are homomorphic so you do not need both. But in terms of learning and exploring, sometimes one gives insight and sometimes the other does so. I believe it is a historical fact that the development of modern algebraic notation and analytic geometry immediately preceded the development of the infinitesimal calculus.

How old is precalculus? It was created in the 20th century, right?