How's your trig? This puzzle is to evaluate the following expression:
6 * ( (sine 1 degree)^2 + (sine 2 degrees)^2 + (sine 3 degrees)^2 + ... + (sine 720 degrees)^2 – 23)
Happy new year to all readers.
Cinelli
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Trig
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Re: Trig
cinelli wrote:How's your trig? This puzzle is to evaluate the following expression:
6 * ( (sine 1 degree)^2 + (sine 2 degrees)^2 + (sine 3 degrees)^2 + ... + (sine 720 degrees)^2 – 23)
Happy new year to all readers.
Cinelli
Oh dear. Neither the 'puter nor anything more obscure than Πῡθαγόρᾱς required.
That's 720 squares. Twice round the circle.
But sin(x) = cos(90-x). We can express the sum as one circle of sines and t'other of cosines. And sin2(x) + cos2(x) = 1. So the sum of all your trig is 360.
I guess 6*(360-23) must be 2022? Hmm, yes, arithmetic confirms it.
Edit: damn, I thought [sup] worked as markup here for those squares, but evidently not. I'll leave it as sin2(x)/etc.
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