How solve this trigo system ?
09-18-2017, 10:12 AM (This post was last modified: 09-18-2017 10:44 AM by Gerson W. Barbosa.)
Post: #2
 Gerson W. Barbosa Senior Member Posts: 1,546 Joined: Dec 2013
RE: How solve this trigo system ?
From the first equation,

cos(y)=cos(x)-1/2

(sin(y))^2=1-(cos(x))^2+cos(x)-1/4

After squaring the second equation and replacing, we get

(cos(x))^4 - (cos(x))^3 - 7/4*(cos(x))^2 + cos(x) + 39/64 = 0

which can be solved by PROOT on the 50g:

[ 1 -1 '-7/4' 1 '39/64' ]

PROOT ->

cos(x) = [ -.411437827766 .911437827766 -1.04903810568 1.54903810568 ]

The first two roots appear to be

'(1-√7)/4' and '(1+√7)/4',

respectively.

Edited to fix the sign of one of the exact solutions.
 « Next Oldest | Next Newest »

 Messages In This Thread How solve this trigo system ? - ggauny@live.fr - 09-18-2017, 08:56 AM RE: How solve this trigo system ? - Gerson W. Barbosa - 09-18-2017 10:12 AM RE: How solve this trigo system ? - ggauny@live.fr - 09-18-2017, 10:45 AM RE: How solve this trigo system ? - Gerson W. Barbosa - 09-18-2017, 10:55 AM RE: How solve this trigo system ? - Gerson W. Barbosa - 09-18-2017, 11:28 AM RE: How solve this trigo system ? - Dieter - 09-18-2017, 12:46 PM RE: How solve this trigo system ? - Dieter - 09-18-2017, 05:48 PM RE: How solve this trigo system ? - AlexFekken - 09-19-2017, 06:36 AM RE: How solve this trigo system ? - Albert Chan - 01-31-2020, 10:48 PM RE: How solve this trigo system ? - Dieter - 09-19-2017, 06:30 PM RE: How solve this trigo system ? - ggauny@live.fr - 09-22-2017, 07:27 AM RE: How solve this trigo system ? - Gerson W. Barbosa - 09-22-2017, 05:05 PM

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