Approximate the function cos(x)
- Ryan Hirst
- 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: http://www.geogebratube.org/material/show/id/37814
- 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.
- 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.