1. Rational Trigonometry

What on earth is Rational Trigonometry?

https://en.m.wikipedia.org/wiki/Rational_trigonometry

I prefer trigonometry as taught in most high school courses.
I have taken the time to watch several videos on this course as taught by professor N J Wildberger on youtube.com and honestly, it makes no sense whatsoever. What do you say? Do you prefer rational trig or trig as taught back in your high school days?

2. Re: Rational Trigonometry

Originally Posted by harpazo
What on earth is Rational Trigonometry?

https://en.m.wikipedia.org/wiki/Rational_trigonometry

I prefer trigonometry as taught in most high school courses.
I have taken the time to watch several videos on this course as taught by professor N J Wildberger on youtube.com and honestly, it makes no sense whatsoever. What do you say? Do you prefer rational trig or trig as taught back in your high school days?
What does ANY mathematics have to do with preference? If it solves necessary problems, it has a place. If it doesn't seem to solve any necessary problem, but will at some time in the future, it has a place. If it is demonstrable quackery, it has no place. If it teaches students to think in a different way (take a noneuclidean geometry course, for example), it has a place. Personally, I much prefer euclidean geometry for building buildings, but this does me little good in cosmology or relativity.

3. Re: Rational Trigonometry

Originally Posted by TKHunny
What does ANY mathematics have to do with preference? If it solves necessary problems, it has a place. If it doesn't seem to solve any necessary problem, but will at some time in the future, it has a place. If it is demonstrable quackery, it has no place. If it teaches students to think in a different way (take a noneuclidean geometry course, for example), it has a place. Personally, I much prefer euclidean geometry for building buildings, but this does me little good in cosmology or relativity.
I'm sure rational trigonometry is important and has a place in the world of math. However, if I ever decide to review trigonometry, I will take the route of MATH FOR DUMMIES or simply watch traditional trig courses online.

4. Re: Rational Trigonometry

I don't see any need for rational trig. It just seems to me to be a waste of time. If you are going to approximate trig functions approximate them. This thing about avoiding square roots is just silly. Either way you are simply doing an approximation. It reminds me of when my students were upset with me because the numbers on my tests didn't come out "nice." Sorry but the acceleration due to gravity is 9.8 m/s^2, not 10 m/s^2.

-Dan

5. Re: Rational Trigonometry

Originally Posted by topsquark
I don't see any need for rational trig. It just seems to me to be a waste of time. If you are going to approximate trig functions approximate them. This thing about avoiding square roots is just silly. Either way you are simply doing an approximation. It reminds me of when my students were upset with me because the numbers on my tests didn't come out "nice." Sorry but the acceleration due to gravity is 9.8 m/s^2, not 10 m/s^2.

-Dan
Your students upset about numbers that do not come out nicely reminds me of an episode in the former tv series Boston Public. In that one particular episode, parents wanted to sue the high school for allowing physics and advanced math into the curriculum. Yes, I expect parents to fight in a court of law because the new generation of students are robotic in nature.
Ridiculous! What do students expect physics to be all semester long? Solve F = ma for m? I really feel bad for future generations of adults that were simply "promoted" from grade to grade without actually learning how to learn.

BTW, I agree with you about rational trigonometry. It's ok by me if professors want to use it in their personal, professional math study time but forcing students to pass such a course makes no sense to me. It leads to more confusion about a course that already is confusing to most students. Students panic at the thought of facing sine, cosine, tangent and the rest.

6. Re: Rational Trigonometry

Well, I didn't panic at trigonometry, but I did panic at decimal fractions, especially the ones that didn't stop somewhere. Needless to say, from number 0-9, I hate 7.

7. Re: Rational Trigonometry

Originally Posted by Monoxdifly
Well, I didn't panic at trigonometry, but I did panic at decimal fractions, especially the ones that didn't stop somewhere. Needless to say, from number 0-9, I hate 7.
All fractions are decimals. I took a math course at City Tech by the title Algebra 2 and Trigonometry (MA185). I got a C without taking the class too seriously. The next course on the list was Precalculus, which I took at Lehman College as an elective.

I got an A minus in the course. This was way back in the Spring 1993 semester. I was 28 years old. I will be 54 in April. We never take time to think about the brevity of life on earth.

I graduated from Lehman College in 1994 and from City Tech in 1990. I allowed the years to go by without truly preparing for life as I know it today. Looking back, I should have majored in math but when I developed a passion for mathematics, I was already several courses into sociology.

It did not make sense to switch from one major to another so close to graduation. I like trigonometry. However, I do not care in the least about rational trigonometry. Go check out the video clips by NJ Wildberger. Insane stuff!!

8. Re: Rational Trigonometry

Originally Posted by topsquark
Sorry but the acceleration due to gravity is 9.8 m/s^2, not 10 m/s^2.
-Dan
And $\pi$ is not 3.2
https://rationalwiki.org/wiki/Indiana_Pi_Bill
...no matter how hard one tries.

9. Re: Rational Trigonometry

Thank you everyone.