Hvordan løser du 3cscA-2sinA-5 = 0?

Svar:

# A = KPI + (- 1) ^ k (pi / 6), Kinz #

Forklaring:

# 3cscA-2sinA-5 = 0 #

# RArr3 / sinA-2sinA-5 = 0 #

# RArr3-2sin ^ 2A-5sinA = 0 #

# RArr2sin ^ 2A + 5sinAcolor (rød) (- 3) = 0 #

# RArr2sin ^ 2A + 6sinA-sinA-3 = 0 #

# RArr2sinA (sinA + 3) -1 (sinA + 3) = 0 #

#rArr (sinA + 3) (2sinA-1) = 0 #

# RArrsinA = -3! I -1,1, sinA = 1 / 2in -1,1 #

# RArrsinA = sin (pi / 6) #

# RArrA = KPI + (- 1) ^ k (pi / 6), Kinz #

# RArrA = KPI + (- 1) ^ k (pi / 6), Kinz #

Svar:

# A = (npi) / 2 + -pi / 3, ninZZ #

#color (hvit) (A) = n90 ^ sirk + -60 ^ sirk, ninZZ #

Forklaring:

Først multipliserer vi alt ved # SinA # siden # CSCA = 1 / sinA # og sinA / sinA = 1 #

#sinA (3cscA-2sinA-5) = sinA (0) #

# 3-2sin ^ 2A-5sinA = 0 #

Erstatning # X = sinA #

# 2 x ^ 2 + 5x-3 = 0 #

#X = (- b + -sqrt (b ^ 2-4ac)) / 2 #

#COLOR (hvit) (x) = (- 5 + -sqrt (5 ^ 2-4 (2 * -3))) / 4 #

#COLOR (hvit) (x) = (- 5 + -sqrt (25 + 24)) / 4 #

#COLOR (hvit) (x) = (- 5 + -sqrt (49)) / 4 #

#COLOR (hvit) (x) = (- 5 + -7) / 4 #

#color (hvit) (x) = (- 5-7) / 4 eller (-5 + 7) / 4 #

#color (hvit) (x) = - 12/4 eller 2/4 #

#color (hvit) (x) = - 3 eller 1/2 #

Derimot, # -1lesinAle1 # så vi må ta #1/2#

# SinA = 1/2 #

# A = arcsin (1/2) = pi / 6- = 30 ^ sirkel, A = (5pi) / 6- = 150 ^ sirk #

# A = (npi) / 2 + -pi / 3, ninZZ #

#color (hvit) (A) = n90 ^ sirk + -60 ^ sirk, ninZZ #