The Seven Deadly Sines
The seven deadly sins of trigonometry: lusting to treat sine as linear, envying logs' tidy inverses, pride in the right-triangle definition, wrath at impossible equations like sin x = 1.5, gluttony for versines and haversines, the avarice of tau evangelists, and the sloth of never evaluating anything by hand.
Transcript
[1] "the LUST for LINEARITY" [Board: sin(2x) = 2 sin x] "I can do this, right? Right?!" "Oh, I want to do it so bad…"
[2] "the ENVY of WELL-BEHAVED INVERSES" [Board: arcsin(sin(x)) ≠ x] "Ugh! Why not? It works for logs and exponentials. Why not me?"
[3] "PRIDE in OLD DEFINITIONS THAT FALL SHORT OF FULL GENERALITY" [Board: sin θ = opp./hyp., with a right triangle] "Ha! Nailed it. Trig is easy."
[4] "the WRATH of DOMAIN AND RANGE ERRORS" [Board: sin(x) = 1.5, x = ???] "YIELD TO ME, INSOLENT EQUATION OR ELSE PERISH"
[5] "the GLUTTONY for WAY MORE TRIG FUNCTIONS THAN ANYONE COULD POSSIBLY HAVE APPETITE FOR" [Board: sec x = 1/cos x; versin x = 1 − cos x; hav x = sin²(x/2)] "Mmm… so needless… so decadent…"
[6] "the AVARICE of TAU EVANGELISTS" [Board: τ = 2π; sin(π/2) = sin(τ/4); e^(τi) = 1] "Ha ha ha! All shall be τ!"
[7] "the SLOTH of NEVER WANTING TO EVALUATE ANYTHING BY HAND" [Board: sin(7π/6) = ?] "I know this is one of the ones that I know." "So what is it?" "Oh, I don't actually know it. I just know that I know it."
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Cartoon by Ben Orlin, Math with Bad Drawings. https://cartoons.mathwithbaddrawings.com/2021-07-19-the-seven-deadly-sines/ (CC BY-NC 4.0)