4.05-tan(x) = cos(x)*3.9

Hello anonymous!

 

4.05-tan(x) = cos(x)*3.9                  [ cosx = 1 / √(1 + tan²x)

4,05-tanx =3,9/√(1+tan²x)

√(1+tan²x) * (4,05-tanx) = 3,9         [ tanx = z

√(1+z²) * (4,05-z) = 3,9                  [ 1. / (4,05 -z)  2. Quadrieren

1+z² = (3,9/(4,05-z))² 

1+z² = 3,9²/(4,05²-8,1z +z²)            [ * (4,05²-8,1z +z²) und gleich ausmultiplizieren

4,05²-8,1z +z² + 4,05²z² -8,1z³ + z^4 = 3,9²

z^4 - 8,1z³ +17,4025z² - 8,1z + 1,1925 = 0

 

http://equationsolver.intemodino.com/de/gleichungen-4-grades-loesen.html

x^4 - 8.1x^3 + 17.4025x^2 - 8.1x + 1.1925 = 0
Die Gleichung hat 2 reelle Lösungen und 2 komplexe Lösungen
x1 = 4.8392373 = z(1)
x2 = 2.6918853 = z(2)
x3 = 0.2844387+0.1031387i
x4 = 0.2844387-0.1031387i

 

z(1) = tan (x1) = 4,8392373

x1 = atan z(1) = 78,3245°

z(2) = tan (x2) = 2,6918853

x2 = atan z(2) = 69,6206°

 

 

 Gruß asinus :- )