I recall as a young math student frequently wondering to myself, “when am I ever going to use this again in life?”
Recently I found the answer to this question. I will use the math skills again when twenty years later my nieces call me to ask how to do their math homework.
I do not think this answer would have satisfied my young math student self.
I both understand and hate this question. It’s a sign that we teach math horribly.
1 – sin²Θ = cos²Θ is a corollary of the Pythagorean Theorem. Imagine any right triangle with a hypotenuse of 1 where Θ is one of the acute angles.
sin Θ is the length of the opposite side (A). cos Θ is the length of the adjacent side (B). And the hypotenuse (C) by definition is 1.
The Pythagorean Theorem is A² + B² = C². So when we plug the values above in we get:
sin²Θ + cos²Θ = 1²
Subtracting sin²Θ from both sides we get:
cos²Θ = 1 – sin²Θ
We teach math as a bunch of arbitrary rules. Believe it or not, I just now figured this proof out. I was able to do this because I have a fundamental understanding of what cosine and sine and all about orthogonality. I don’t need to memorize these rules because I have learned how they actually work and what they actually mean. That is what we should teach.
I also calculated the golden ratio before I knew there was a golden ratio.
I laughed very hard at this post. As someone who struggles with the way math is taught these days, I can very much sympathize here.
Thanks for sharing. I needed a laugh today.