Odd Angles Formula Trivia
12-20-2018, 05:38 PM (This post was last modified: 08-13-2019 03:36 PM by Albert Chan.)
Post: #1
 Albert Chan Senior Member Posts: 2,142 Joined: Jul 2018
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)
 « Next Oldest | Next Newest »

 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

User(s) browsing this thread: 1 Guest(s)