trigonométria
Hola por favor necesito ayuda con estas ecuaciones trigonometricas
Resuelve las siguientes ecuaciones para 0 < x < 2
a) sen3x - 2 = -3sen3x
b) senx(2 - senx) = cos2x
c) cosx - 2sen2x + 1 = 0
d) sen2x = senx
Respuestas
Respuesta dada por:
5
a)
sen3x + 3sen3x = 2
4sen3x = 2
sen3x = 2/4
sen3x = 1/2
sen3x = sen30
3x = 30
x = 30/3
x = 10
b)
2senx - sen²x = cos2x
2senx - sen²x = cos²x - sen²x simplificamos -sen²x
2senx = cos²x
2senx = 1- sen²x
sen²x + 2sen +1 = 1 +1
(senx + 1)² = 2
senx + 1 = √2 y senx + 1 = -√2
senx = -1+√2 senx = -1 - √2
c)
cosx - 2senx.cosx + sen²x+cos²x = 0
cosx = (senx + cosx)²
cosx = senx + cosx , -cosx = senx + cosx
0 = senx -2cosx = senx
sen0 = senx -2 = senx/cosx
0 = x -2 = tgx
d) sen2x = senx
2senx.cosx = senx
cosx = 1/2
cosx = cos60
x = 60
sen3x + 3sen3x = 2
4sen3x = 2
sen3x = 2/4
sen3x = 1/2
sen3x = sen30
3x = 30
x = 30/3
x = 10
b)
2senx - sen²x = cos2x
2senx - sen²x = cos²x - sen²x simplificamos -sen²x
2senx = cos²x
2senx = 1- sen²x
sen²x + 2sen +1 = 1 +1
(senx + 1)² = 2
senx + 1 = √2 y senx + 1 = -√2
senx = -1+√2 senx = -1 - √2
c)
cosx - 2senx.cosx + sen²x+cos²x = 0
cosx = (senx + cosx)²
cosx = senx + cosx , -cosx = senx + cosx
0 = senx -2cosx = senx
sen0 = senx -2 = senx/cosx
0 = x -2 = tgx
d) sen2x = senx
2senx.cosx = senx
cosx = 1/2
cosx = cos60
x = 60
Jbiehl2003:
MUUUCHAAAS GRACAIS !!! enserio me salvaste el día :D
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