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Jimmy
Posts:
6
Registered:
2/18/06
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Re: Trigonometry challenge
Posted:
Feb 22, 2006 3:14 AM
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Thank you for your candor.
It appears you are proposing students learn the rational trigonometry theory as well as classical trigonometry or some parts thereof. That is, students use the rational trig for solving only triangle-related problems, and use the classical trig for solving circular or rotational problems, or for converting from rational trig?s nonlinear units to classical trig?s linear units (such as when working with vectors within a linear system of measure).
1. You state one of the principle advantages of rational trigonometry is that it easier for students to calculate rational answers, they being more accurately expressed numerically. But one notices that rational trig generally must express answers in terms of the square root function which only gives the appearance of a rational result. When the function is evaluated it generally produces an irrational number.
Classical trigonometry, on the other hand, can express its answers in terms of the sine function and square root function which too gives the appearance of a rational result. Only after the functions are evaluated do they produce an irrational number.
Why are we making a distinction and claiming that rational trigonometry produces rational results and is more accurate, when the claim can also be made for classical trigonometry?
2. Unlike classical trigonometry, when one examines the calculations required by rational trigonometry, it often requires the student to solve simultaneous quadratic or linear equations and/or use the quadratic formula. In contrast, classical trigonometry can achieve the same rational result (as described above), but without the having to solve the simultaneous quadratic or linear equations or deal with the quadratic formula. How is it that rational trigonometry is easier?
I reworked the same four problems you present in your paper, ?Survivor: the Trigonometry Challenge?, using more appropriate classical formulas, and in all four problems the classical trigonometry calculations were decidedly less and easier when expressed rationally. If calculators were allowed on the island, the classical trigonometry would still clearly win even after evaluating the functions. BTW, the second problem requires the classical guy to calculate the angle to determine its sine, when it was unnecessary.
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