as far as stupid teachers, my 5th grade math teacher was rather, um, liberal arts oriented.
We were taking fractions and turning them into decimals and visa-versa. Her method for going from fractions to decimals was to take the denominator, muliply it by the whole
number that will get it closest to 100, and then multiply the numerator by the same number.
Now, my mom was a math major, and my dad is an electrical engineer (needless to say, I knew basic math and science before I could tie my show laces) so I raised my hand and asked if it would just be easier and simpler to divide. I was told I was wrong, and that didn't turn the fraction into a decimal. WTF? So, I demonstrated this principle with 1/4, 1/5, 1/2... how it was faster, and more accurate than her method. I was told, again, that I was wrong. Fine. Let her be an idiot.
So, 10 or so minutes later, she starts "showing" us how to make decimals into fractions. She said that .05 is 1/16. Again, I raise my hand, and said that it's not 1/16, that it's 1/20. She said I was wrong because the book said it was 1/16. Obviously a typo. I showed her and the class that it was 1/20 using the methods my parents had taught me. She made me sit outside for the rest of the day.
As far as sin, cos, and tan, this is what my calc teacher in high school taught me for the numbers:
so, all I have to remember is 0, 1, 2, 3, 4 ... 4, 3, 2, 1, 0, and how to divide fractions.
"YES. DO IT WITH CONFIDENCE" ~fortune cookie