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A comment on Obsolete trig functions and why we don't use them anymore (2013). Parent comment

Re:Obsolete trig functions and why we don't use them anymore... by sriku on Thursday December 03, 2020 @10:09AM (#25289521)
You don't need to treat "[cos(x)]^2 + [sin(x)]^2 = 1" separately either.

e^(iθ) times e^(-iθ) = e^(iθ-iθ) = e^0 = 1 = (cosθ+isinθ)(cosθ-isinθ) = cos²θ + sin²θ

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Re:Obsolete trig functions and why we don't use them anymore... by josephcsible on Thursday December 03, 2020 @11:03AM (#25290197)
Sure, this takes "[cos(x)]^2 + [sin(x)]^2 = 1" off the list, but doesn't it require you to put "cos(-x) = cos(x)" and "sin(-x) = -sin(x)" on it, to get "(cosθ-isinθ)" from "e^(-iθ)"?
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Re:Obsolete trig functions and why we don't use them anymore... by evanb on Thursday December 03, 2020 @11:11AM (#25290315)
Only if you forget about how complex conjugation works. (e^-ix) = (e^ix)* = cos x - i sin x
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Re:Obsolete trig functions and why we don't use them anymore... by sriku on Thursday December 03, 2020 @09:16PM (#25298165)
As indicated in the other reply, think of the minus as changing the sign of i instead of x.
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