I never bothered to memorize trig equivalences. Instead, I just reduced sine, cosine, and tangent (and their inverses) to ratios of the sides of a triangle, and then used the Pythagorean theorem.
Well, it’s so much easier and more robust that way! Instead of a long list of confoundingly similar equations, you’re left with a single clear understanding of why trigonometry works. After that you can memorize a few formulas as shortcuts if it helps.
Of course this principle completely breaks down when you start working with a child who’s already convinced that they can’t do math—or with a group of 30 kids at once, a third of whose mathematical intuitions will be far enough from the textbook norm that no one teacher has enough time to guide them through to that first epiphany.
I never bothered to memorize trig equivalences. Instead, I just reduced sine, cosine, and tangent (and their inverses) to ratios of the sides of a triangle, and then used the Pythagorean theorem.
Well, it’s so much easier and more robust that way! Instead of a long list of confoundingly similar equations, you’re left with a single clear understanding of why trigonometry works. After that you can memorize a few formulas as shortcuts if it helps.
Of course this principle completely breaks down when you start working with a child who’s already convinced that they can’t do math—or with a group of 30 kids at once, a third of whose mathematical intuitions will be far enough from the textbook norm that no one teacher has enough time to guide them through to that first epiphany.