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I've been using all those trig identies on and off but I seemingly tend to forget them even after using them time and time again. Does anyone have an idea on how to remember the most important (I'm talking about sum, product, double angle,...)?

Hue Ma
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  • Some of them are easy to remember including the most important one : $\sin^2(x)+\cos^2(x)=1$. Some of them can be derived using Euler's formula. – Peter Aug 30 '22 at 17:13
  • Personally, I struggle with them a lot too and found what helped me most was just rederiving them on the spot when I needed them and I was unable to look them up. To do so, I would use the complex analysis definitions of sine and cosine: $\sin(z) = \frac{e^{iz}-e^{-iz}}{2i}$ and $\cos(z) = \frac{e^{iz}+e^{-iz}}{2}$. If you look at $\sin(a+b)$ with this you can rearrange and factor the result and find the identity that way. – JMoravitz Aug 30 '22 at 17:13
  • That's a genius idea, ima look into that – Hue Ma Aug 30 '22 at 17:14
  • @JMoravitz It is definitely helpful for those who have had rudimentary exposure to complex variables, but for high school students or casual people, they may not understand (or appreciate) the power of complex variables and want to keep things simple. If they don't understand the function of $\sqrt {-1}$, then Euler will be useless and it is best left out. – bjcolby15 Aug 30 '22 at 17:33
  • Rote learning of trigonometric identities is madness IMHO. If you are in a learning situation where you are required to have memorised such identities, then challenge your teacher to justify the thinking behind the question. – Rob Arthan Aug 30 '22 at 21:22

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