Odgovor:
Glej spodaj
Pojasnilo:
# cos2θ + 3cosθ + 2 = 0 #
Uporabi dvojni kotični kosinus:
# (2cos ^ 2theta-1) + 3costheta + 2 = 0 #
# 2cos ^ 2theta + 3costheta + 1 = 0 #
# 2cos ^ 2theta + 2costheta + costheta + 1 = 0 #
# 2costheta (costheta + 1) +1 (costheta + 1) = 0 #
# (2costheta + 1) (costheta + 1) = 0 #
# costheta = -1 / 2 #
# theta = 120 ^ @, 240 ^ @ #
# costheta = -1 #
# theta = 180 ^ @ #
graf {cos (2x) + 3cosx + 2 -10, 10, -5, 5}
Odgovor:
Z dvojno kotno formulo jo masiramo v oblike #cos theta = cos a # in dobite
#theta = pm 120 ^ circ + 360 ^ Circ k ali theta = 180 ^ circ + 360 ^ circ k #
Pojasnilo:
Formula dvojnega kota za kosinus je
# cos (2 theta) = 2 cos ^ 2 theta - 1 #
#cos (2 theta) + 3 cos theta + 2 = 0 #
# 2 cos ^ 2 theta + 3 cos theta + 1 = 0 #
# (2 cos theta + 1) (cos theta + 1) = 0 #
#cos theta = -1 / 2 # ali #cos theta = -1 #
Tako daleč, zdaj ne zmešaj. Zapomni si #cos x = cos a # ima rešitve #x = pm a + 360 ^ circ k # za celo število # k #.
#cos theta = cos 120 ^ circ ali cos theta = cos (180 ^ circ) #
#theta = pm 120 ^ circ + 360 ^ Circ k ali theta = pm 180 ^ circ + 360 ^ circ k #
The # pm # v resnici ne pomaga pri # 180 ^ circ # tako smo pristali
#theta = pm 120 ^ circ + 360 ^ Circ k ali theta = 180 ^ circ + 360 ^ circ k #
Preverite:
Preverite eno in pustite splošni pregled. # theta = -120 + 360 = 240 ^ circ.
# cos (2 (240)) + 3 cos (240) + 2 = cos (120) + 3 cos (240) + 2 = -1/2 + 3 (-1/2) + 2 = 0 quad sqrt #
