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I generally just know that any trig formula can be converted to quite a few different other ones visa trig identities. Whether a certain expression is more or

I generally just know that any trig formula can be converted to quite a few different other ones visa trig identities. Whether a certain expression is more or less complex than another is a matter of perspective and context. If I'm stuck with a trig function I don't know what to do with, I just look on Wikipedia for a trig identity and don't worry about derivations or memorization. This trick is good for exam settings though! My memory is terrible so I always relied on tricks like this in school

lopmotr 6y ago
What kind of exam requires you to memorize trig identities? Were they trying to prepare you for a world without paper or computers to look them up on? Or to be a smidgen faster at hand calculations?
- jacobolus 6y ago
  > Were they trying to prepare you for a world without paper or computers Yes, most high schools spend a few months teaching “trigonometry” as a system for simplifying formulas that was primarily useful historically to save time for human calculators working with pen/paper and a printed lookup table. In the modern world this is entirely anachronistic and the content could be profitably compressed down to a couple weeks, with the saved time spent on something else. The main remaining utility is as rather cumbersome, unpleasant, and unenlightening algebra practice.
  - gmadsen 6y ago
    I think it would be enlightening but rarely done in school, is focus on the geometry of it and how the relationships are connected, such as https://math.wikia.org/wiki/Unit_circle?file=Unit_circle_indentities.png https://math.wikia.org/wiki/Unit_circle?file=Unit_circle_ind...
- lynndotpy 6y ago
  I always understood the memorization part as a stopgap to truly understanding them. In the same sense that doing this work by hand will build depth of understanding, I know that remembering the trig identities came before really understanding their relationships. And that also came far before I could truly understand Euler's formula, radians, etc.

lopmotr 6y ago

What kind of exam requires you to memorize trig identities? Were they trying to prepare you for a world without paper or computers to look them up on? Or to be a smidgen faster at hand calculations?

jacobolus 6y ago
> Were they trying to prepare you for a world without paper or computers Yes, most high schools spend a few months teaching “trigonometry” as a system for simplifying formulas that was primarily useful historically to save time for human calculators working with pen/paper and a printed lookup table. In the modern world this is entirely anachronistic and the content could be profitably compressed down to a couple weeks, with the saved time spent on something else. The main remaining utility is as rather cumbersome, unpleasant, and unenlightening algebra practice.
- gmadsen 6y ago
  I think it would be enlightening but rarely done in school, is focus on the geometry of it and how the relationships are connected, such as https://math.wikia.org/wiki/Unit_circle?file=Unit_circle_indentities.png https://math.wikia.org/wiki/Unit_circle?file=Unit_circle_ind...
lynndotpy 6y ago
I always understood the memorization part as a stopgap to truly understanding them. In the same sense that doing this work by hand will build depth of understanding, I know that remembering the trig identities came before really understanding their relationships. And that also came far before I could truly understand Euler's formula, radians, etc.