How solve this trigo system ?

09182017, 12:46 PM
(This post was last modified: 09182017 01:48 PM by Dieter.)
Post: #6




RE: How solve this trigo system ?
(09182017 08:56 AM)ggauny@live.fr Wrote: I would like solve my exercize with my Prime but I dont' know As Gerson already noted, you can use trigonometric identities. For instance the most simple one: sin²x + cos²x = 1 so that sin x = √(1–cos²x). Now use this in the second equation and get (after squaring) (1–cos²x) * (1–cos²y) = (3/8)² Since cos x = cos y + 1/2 you get [1 – (cos y + 1/2)²] * (1 – cos²y) = 9/64 I was too lazy to solve this manually, so I just fed it to the Solver of my HP35s. Note that you do not solve for y but for cos y here. Let's call the cosine "c": EQN (1–(C+0,5)^2) x (1–C^2) = 9÷64 If we assume that c is somewhere between 0 and 1, these two guesses yield C=0,411437827766. So y = arccos c = 65,704811° and x = arccos(c+1/2) = 24,295189° (which is 90°–y). Starting with –1 and 0 as initial guesses returns C=–0,911437827766, leading to y = 155,704811° and x = 114,295189°. No Prime required here. ;) But of course you can also use the Prime's solver with the above equation. Note 1: the exact values for c are –¼ · (1±√7). Note 2: the solver equation can be written as C^{4} + C^{3} – 7/4 C^{2} – C + 39/64 = 0. Compare this with Gerson's quartic equation above. Dieter 

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Messages In This Thread 
How solve this trigo system ?  ggauny@live.fr  09182017, 08:56 AM
RE: How solve this trigo system ?  Gerson W. Barbosa  09182017, 10:12 AM
RE: How solve this trigo system ?  ggauny@live.fr  09182017, 10:45 AM
RE: How solve this trigo system ?  Gerson W. Barbosa  09182017, 10:55 AM
RE: How solve this trigo system ?  Gerson W. Barbosa  09182017, 11:28 AM
RE: How solve this trigo system ?  Dieter  09182017 12:46 PM
RE: How solve this trigo system ?  Dieter  09182017, 05:48 PM
RE: How solve this trigo system ?  AlexFekken  09192017, 06:36 AM
RE: How solve this trigo system ?  Albert Chan  01312020, 10:48 PM
RE: How solve this trigo system ?  Dieter  09192017, 06:30 PM
RE: How solve this trigo system ?  ggauny@live.fr  09222017, 07:27 AM
RE: How solve this trigo system ?  Gerson W. Barbosa  09222017, 05:05 PM

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