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Golden Spike National Historic Site, Promontory, Utah

Photo by Vickie Kelly, 1999. Greg Kelly, Hanford High School, Richland, Washington. 7.4 Day 1 Lengths of Curves. Golden Spike National Historic Site, Promontory, Utah. Length of Curve (Cartesian). Lengths of Curves:.

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Golden Spike National Historic Site, Promontory, Utah

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  1. Photo by Vickie Kelly, 1999 Greg Kelly, Hanford High School, Richland, Washington 7.4 Day 1 Lengths of Curves Golden Spike National Historic Site, Promontory, Utah

  2. Length of Curve (Cartesian) Lengths of Curves: If we want to approximate the length of a curve, over a short distance we could measure a straight line. By the pythagorean theorem: We need to get dx out from under the radical.

  3. Now what? This doesn’t fit any formula, and we started with a pretty simple example! The TI-89 gets: Example:

  4. If we check the length of a straight line: Example: The curve should be a little longer than the straight line, so our answer seems reasonable.

  5. Y Y F4 ENTER ENTER ENTER STO Example: You may want to let the calculator find the derivative too: Important: You must delete the variable y when you are done! 4

  6. Example:

  7. X ENTER STO If you have an equation that is easier to solve for x than for y, the length of the curve can be found the same way. Notice that x and y are reversed.

  8. Y X F4 ENTER Don’t forget to clear the x and y variables when you are done! 4 p

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