Antwoord:
# X = 2npi + - (2pi) / 3 #
Uitleg:
# Rarrcos2x + 5cosx + 3 = 0 #
# Rarr2cos ^ 2x-1 + 5cosx + 3 = 0 #
# Rarr2cos ^ 2x + 5cosx + 2 = 0 #
# Rarr2cos ^ 2x + + 4cosx cosx + 2 = 0 #
# Rarr2cosx (cosx + 2) 1 (cosx + 2) = 0 #
#rarr (2cosx + 1) (cosx + 2) = 0 #
Een van beide, # 2cosx + 1 = 0 #
# Rarrcosx = -1/2 = cos ((2pi) / 3) #
# Rarrx = 2npi + - (2pi) / 3 # waar # NrarrZ #
Of, # Cosx + 2 = 0 #
# Rarrcosx = -2 # wat onaanvaardbaar is.
Dus de algemene oplossing is # X = 2npi + - (2pi) / 3 #.
Antwoord:
# Theta = 2kpi + - (2pi) / 3, Kinz #
Uitleg:
# Cos2theta + 5costheta + 3 = 0 #
# ^:. 2cos 2teta-1 + 5costheta + 3 = 0 #
# ^:. 2cos 2teta + 5costheta + 2 = 0 #
# ^:. 2cos 2teta 4costheta + + costheta + 2 = 0 #
#:. 2costheta (costheta + 2) 1 (costheta + 2) = 0 #
#:. (costheta + 2) (2costheta + 1) = 0 #
# => costheta = -2! in -1,1, of costheta = -1 / 2 #
# => Costheta = cos (pi-pi / 3) = cos ((2pi) / 3) #
# Theta = 2kpi + - (2pi) / 3, Kinz #
Antwoord:
Gebruik # cos2theta = 2 (costheta) ^ 2-1 # en de algemene oplossing van #costheta = cosalpha # is # Theta = 2npi + alfa #; # N Z #
Uitleg:
# Cos2theta + 5costheta + 3 #
# = 2 (costheta) ^ 2-1 + 5costheta + 3 #
# = 2 (costheta) ^ 2 + 5costheta + 2 #
#rArr (costheta + 1/2) (costheta + 2) = 0 #
Hier #costheta = -2 # is niet mogelijk
Dus we vinden alleen de algemene oplossingen van # Costheta = -1/2 #
# RArrcostheta = (2pi) / 3 #
#:. theta = 2npi + - (2pi) / 3; n Z #
