I liked solving quadratic problems, polynomials, or writing theorems or proofs when it came to solving geometry problems. I loved graphing lines , equations, functions, and finding solutions,. I even liked statistics. That all made sense or seemed logical. Even as I got much older and took 4 semesters of Chemistry and Organic chemistry for fun (and torture, I suppose), a lot more math, including quantum physics stuff, figuring out things about sub-atomic particles, that could not be seen, those items made more sense to me than trigonometry. Trigonometry class always gave me pause and frustration. Just use the charts, learn the functions, follow the rules, memorize what we are teaching, solve the problems, take the tests, and blindly believe it. Then try to forget the frustrating experience. It didn’t really make much sense or it did not all fit together like all the other fun stuff in math, including Matrices, which could be applied to a bunch of problem solving including algebra, abstract algebra, and Analytical Chemistry.
I took trigonometry again, in college, 10 years after high school, to see if I could visit the subject matter and understand it a second time around.
I still was not grasping the Trigonometry math the way we were taught. Triangular problems solved with circular functions. The trigonometry solving skills in place for 2,000 - 3,000 years or so ago, back to before Ptolemy, may have been wrong. At least according to an Australian academic, Dr Norman Wildberger, who believes that trigonometry solving can be simplifed to algebraic solutions, and with much greater accuracy, and a lot less frustration?.
I already feel like believing him.
From New trigonometry is a sign of the times :
Rational trigonometry replaces sines, cosines, tangents and a host of other trigonometric functions with elementary arithmetic.
He adds:
So teachers have resigned themselves to teaching students about circles and pi and complicated trigonometric functions that relate circular arc lengths to x and y projections – all in order to analyse triangles. No wonder students are left scratching their heads,
But with no alternative to the classical framework, each year millions of students memorise the formulas, pass or fail the tests, and then promptly forget the unpleasant experience.
I *never* forgot the unpleasant experience. I passed the class, though I did not like the material, and did not feel like I learned anything.
According to Wildberger, learning 5 main rules, will get you there. I believe or would like to believe this is true. IT would help solve my confusion and frustration with trig. Wildberger’s book on the subject, Divine Proportions: Rational Trigonometry to Universal Geometry, published by Wild Egg books, will launch this week.
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