Visualizing the derivative of sin(x)pic.twitter.com/QqNRaxkjbg
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A fun way to remember the derivatives of sine and cosine is to set equal the Real and Imaginary parts of 𝑑/𝑑𝑥 (eⁱˣ )pic.twitter.com/2ErvL6oCKR
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Man, I literally never learned the far majority of trig identities. I think using exponentials for basically any trig stuff is the way to go. Usually I have to derive identities on the fly when teaching first years though
But I strongly advocate for this trick, applied broadly -
yea! i came up with this one in traffic lmao
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nah fam i just remember the cosine derivative is negative and run with it
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Another fun way is to visualize the graphs of sine and cosine and then mentally graph their slopes.
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A fun way to use the same trick for Kepler’s laws from Newton’s laws. In Dutch, but the formulas will remain universal, to the dismay of some Stanford professors perhaps. http://www.nieuwarchief.nl/serie5/pdf/naw5-2007-08-4-270.pdf …
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I always use the memo, Derivative = I let the function « derive » clockwise
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Or geometrically likewise perpendicular.
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