Approximate the function cos(x)

Ryan Hirst
  1. The red arc is the 2nd order Bezier curve: p(t)= A + 2(B-A)t + (C-2B+A)t², 0≤t≤1. To find the vertex, focus, and parabola equation:
  2. To convert this to an equation in x: Solve for t. Then The conversion can be put off as long as possible. A, B,C, are sufficient to retrieve both the original function and calculate an approximation.
  3. The analysis graphs don't prove the results. However, it should be clear that we only need to establish Does the parabola arc cross cos(x)? in the neighborhood of a point where they are tangent.
________ {The zeros of a polynomial}