Use the bisection method to find a root of the function

f(x) = cos(x) - x.

Using JKGraph:

Since f(0) > 0 and f(1) < 0, we use the bisection method on the closed interval [0,1].

  1. On the Formulas menu, choose Function Formula: Y=F(X).
  2. At the prompt F(X) = , type in
  3. Click on the button Edit Solve Domain.
  4. At the prompt, First Point X-Coordinate:, enter 0.
  5. At the prompt, Second Point X-Coordinate:, enter 1.
  6. At the prompt, Solution Method, click on Successive Bisections.
  7. At the prompt, Output Format, click on Graphical Output.
  8. At the prompt, Automatic/Manual, click on Automatic Animation.
  9. Click on the OK button.
  10. Click on the World Graph Domain button.
  11. At the prompt, Graph X Minimum Value:, enter 0.
  12. At the prompt, Graph X Maximum Value:, enter 1.
  13. At the prompt, Graph Y Minimum Value:, enter -1.
  14. At the prompt, Graph Y Maximum Value:, enter 1.
  15. Click on the OK button twice and you will see the graph of the function.
  16. Finally, click on the Solve button and you will see the following graph.

    The approximation of the root appears at the bottom of the screen.