in context: how to solute a geo-math equation

Hallo, - may be someone here is a little bit more fit in trigonometrical mathmatic and can give an advise...

The following formular is given:
-tan(a)*tan(l)*sin(o) = cos(r) + sin(r)*tan(a)*cos(o)
a, l and o are known

I cannot figure out how to solute this equation for r.
Thanks to everyone who's answering
martin

Hi everybody,

Happy to visit the forum today.

Here is the solution found by my friend Noel who works with me in the same service ( not in my Atlas Couscous where the math formula to find the best sauce is a secret and is more complicated :lol: )


cos(R) = sin(R)*tang(A)*cos(O)+tang(A)*tang(L)*sin(O)
cos²(R) = sin²(R)*tang²(A)*cos²(O)+tang²(A)*tang²(L)*sin²(O)
+ 2 sin(R)*tang²(A)*cos(O)*sin(O)*tang(L)

0 = sin²(R)*(1+tang²(A)*cos²(O)
+ 2sin(R)*tang²(A)*cos(O)*sin(O)*tang(L)
- 1 + tang²(A)*tan²(L)*sin²(O)

X = ( 2 tang²(A)*cos(O)*sin(O)*tang(L))²
- 4(1+tang²(A)*cos²(O))(tang²(A)*tang²(L)*sin²(O)-1)

sin(R) = ( - 2 ( tang²(A)*cos(O)*sin(O)*tang(L) (+ or -) squareroot(X) ) /
2(1+tang²(A)*cos²(O))

R = arcsin( of all this... )





Hope this will help
I did no test, but I think you will find easilly your algorithm
(+ or - ) means that there 2 solutions , you have to test wich one is correct , try (+) and (-) .


Mohamed
www.atlascouscous.com

whow...
To quadrate the formula is something I surely would never had been done... I will test it tomorrow - it'll be a hard job because I really need to conceive it and that means to get some school stuff back in my mind...
I'll contact you if I find a secret recipe for a sauce.
Thank you very much
martin

Hi Mohamed,
...got it and it works!!!!!

Thanks a lot for your or your friends effort!
martin

Hi Martin,

I used some trigonometrical tricks with Mappoint, but I don't understand the use of your formula! Never mind, I will look at this another time!

Ciao

...it is to draw nautical lines in the maps... for sailing away...
see you