Odd Angles Formula Trivia
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12-20-2018, 05:38 PM
(This post was last modified: 08-13-2019 03:36 PM by Albert Chan.)
Post: #1
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Odd Angles Formula Trivia
Reading Multiple Angle Formulas, noticed some pattern for odd angles
Let s = sin(x), c = cos(x): sin(-x) = -s cos(-x) = c sin(x) = s cos(x) = c sin(3 x) = -(4 s³ - 3 s) cos(3 x) = 4 c³ - 3c sin(5 x) = 16 s5 - 20 s³ + 5 s cos(5 x) = 16 c5 - 20 c³ + 5 c Challenge: prove above pattern continues: if sin(4nx ± x) = f(s,c), then cos(4nx ± x) = ± f(c,s) |
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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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