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Comment by tgb | Hacker News Reader

Hmm it's been my opinion that most of the time that trigonometry is used, one should work with vectors instead. This goes doubly for inverse trig. If you have trig then inverse trig, you can almost always turn it into a geometrically meaningful vector operation and avoid the difficulty of handling the ambiguous range of inverse trig functions properly. Remember your sohcahtoa for doing this.

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Absolutely. Trigonometric functions are quite slow. Here’s an example on how to implement angles without trigonometric functions: https://gist.github.com/Const-me/46f90ce7fc2bc65dc12a41442ed...

And for cases when you need to multiply angles by a scalar (e.g. to interpolate between two angles), quaternions is the way to go: https://en.wikipedia.org/wiki/Quaternions_and_spatial_rotati...

"...Remember your sohcahtoa..."

My what?

Oh, you mean Oscar Had A Headache Over Algebra.

I'd love to find a math cheat sheet poster with comparative mnemonics for the office wall. There are a ton of them. I imagine they vary depending on the pedigree of the teacher.

Just in case you or someone else doesn't know what soh-cah-toa represents:

- Soh: sin θ = o/h

- Cah: cos θ = a/h

- Toa: tan θ = o/a

Where "θ" is the angle, "o" is the side opposite of the angle, "a" is the side adjacent to the angle, and "h" is the hypotenuse.

Or for the visually inclined:

         +
        /|
     h / |
      /  | o
     /θ  |
    +----+
       a

we were taught... The Cat Sat On An Orange And Howled Horribly

We were taught "Some Old Hippy Caught Another Hippy Tripping on Acid"

This seems to be the only mnemonic in this thread that matches soh-cah-toa, and it's quite memorable, so kudos to your teacher!

The one we were taught was "Silly old Hitler caused awful headaches to our allies".

"All Stations To Central" is the mnemonic I still remember as you progress around quadrants of circle:

Whenever I pass through central station in Sydney I hear my high school math teacher's voice:

Less than PI/2 "All are positive PI/2 through to PI "Sin is positive" PI through to 3/2 PI "Tan is positive" 3/2 PI through to 2PI "Cos is positive"

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