Odd Angles Formula Trivia
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08-15-2019, 03:42 PM
(This post was last modified: 09-23-2019 09:09 PM by Albert Chan.)
Post: #5
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RE: Odd Angles Formula Trivia
(08-15-2019 01:55 AM)Albert Chan Wrote: x = 1/5³ = 0.008 // reduced angle, in radian A trick to improve accuracy, by defining cosm1(x) = cos(x) - 1 Polynomial to scale cosm1(x) to cosm1(5x) = T5(x+1) - 1 = 25x + 100x^2 + 140x^3 + 80x^4 + 16x^5 = ((4*x + 10)*x + 5)^2 * x cosm1(x) ≅ -x^2/2 + x^4/24 = -0.00003199982933 cosm1(0.04) = -0.0007998933389, error = -1 ULP cosm1(0.20) = -0.01993342215, error = -1 ULP cosm1(1.00) = -0.4596976940, error = -1 ULP cos(1) = cosm1(1) + 1 = 0.5403023060, error = -1 ULP |
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Messages In This Thread |
Odd Angles Formula Trivia - Albert Chan - 12-20-2018, 05:38 PM
RE: Odd Angles Formula Trivia - Albert Chan - 12-21-2018, 01:10 PM
RE: Odd Angles Formula Trivia - Albert Chan - 08-14-2019, 01:54 PM
RE: Odd Angles Formula Trivia - Albert Chan - 08-15-2019, 01:55 AM
RE: Odd Angles Formula Trivia - Albert Chan - 08-15-2019 03:42 PM
RE: Odd Angles Formula Trivia - Albert Chan - 12-15-2019, 01:03 AM
RE: Odd Angles Formula Trivia - Albert Chan - 12-15-2019, 01:49 AM
RE: Odd Angles Formula Trivia - Albert Chan - 01-22-2020, 12:45 AM
RE: Odd Angles Formula Trivia - Albert Chan - 10-13-2021, 03:40 AM
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