Re:Common Errors in Undergraduate Mathematics (2009)
by roberto on Sunday June 25, 2017 @11:44AM
(#14630526)
My algebra teacher in college did the first mistake. I still remember it after 21 years:
1. She was reducing some formula, and got it down to cos(a - 0), which is obviously cos(a). The problem is, her cheat sheet had the solution as sin(a).
2. She "expanded" to cos(a - 0) = cos(a) - cos(0)
3. We know cos(0), so this leads us to cos(a) - 1
4. This is where she got stuck. After thinking for a long time she wrote on the board: "(from trigonometry) cos(a) - 1 = sin(a)"
5. Final answer: sin(a)
I went up to the board and explained step 2 was wrong and how she should've done it, and I explained that step 4 was wronger, because that would mean that for some angles cos/sin would be outside the [-1, 1] range.
She said, "let's try your way then, young man", and doing the expansion on cos(a - 0) got it to cos(a). She then proceed to say I was wrong, because the answer had to be sin(a).
I still thank her for teaching me to question authority.
1. She was reducing some formula, and got it down to cos(a - 0), which is obviously cos(a). The problem is, her cheat sheet had the solution as sin(a). 2. She "expanded" to cos(a - 0) = cos(a) - cos(0) 3. We know cos(0), so this leads us to cos(a) - 1 4. This is where she got stuck. After thinking for a long time she wrote on the board: "(from trigonometry) cos(a) - 1 = sin(a)" 5. Final answer: sin(a)
I went up to the board and explained step 2 was wrong and how she should've done it, and I explained that step 4 was wronger, because that would mean that for some angles cos/sin would be outside the [-1, 1] range.
She said, "let's try your way then, young man", and doing the expansion on cos(a - 0) got it to cos(a). She then proceed to say I was wrong, because the answer had to be sin(a).
I still thank her for teaching me to question authority.