Kako najti natančno vrednost COS (SIN ^ -1 4/5 + TAN ^ -1 5/12)?

Odgovor:

#rarrcos (sin ^ (- 1) (4/5) + tan ^ (- 1) (5/12)) = 16/65 #

Pojasnilo:

Let #sin ^ (- 1) (4/5) = x # potem

# rarrsinx = 4/5 #

# rarrtanx = 1 / cotx = 1 / (sqrt (csc ^ 2x-1)) = 1 / (sqrt ((1 / sinx) ^ 2-1)) = 1 / (sqrt ((1 / (4/5)) ^ 2-1)) = 4/3 #

# rarrx = tan ^ (- 1) (4/3) = sin ^ (- 1) = (4/5) #

Zdaj,

#rarrcos (sin ^ (- 1) (4/5) + tan ^ (- 1) (5/12)) #

# = cos (tan ^ (- 1) (4/3) + tan ^ (- 1) (5/12)) #

# = cos (tan ^ (- 1) ((4/3 + 5/12) / (1- (4/3) * (5/12)))) #

# = cos (tan ^ (- 1) ((63/36) / (16/36))) #

# = cos (tan ^ (- 1) (63/16)) #

Let #tan ^ (- 1) (63/16) = A # potem

# rarrtanA = 63/16 #

# rarrcosA = 1 / secA = 1 / sqrt (1 + tan ^ 2A) = 1 / sqrt (1+ (63/16) ^ 2) = 16/65 #

# rarrA = cos ^ (- 1) (16/65) = tan ^ (- 1) (63/16) #

#rarrcos (sin ^ (- 1) (4/5) + tan ^ (- 1) (5/12)) = cos (tan ^ (- 1) (63/16)) = cos (cos ^ (- 1) (16/65)) = 16/65 #

Kako najdete natančno vrednost greha (cos ^ -1 (sqrt5 / 5))?

Sin (cos ^ -1 (sqrt (5) / 5)) = (2sqrt (5)) / 5 Naj cos ^ -1 (sqrt (5) / 5) = A potem cosA = sqrt (5) / 5 in sinA = sqrt (1-cos ^ 2A) = sqrt (1- (sqrt (5) / 5) ^ 2) = (2sqrt (5)) / 5 rarrA = sin ^ -1 ((2sqrt (5)) / 5) Zdaj, greh (cos ^ -1 (sqrt (5) / 5)) = sin (sin ^ -1 ((2sqrt (5)) / 5)) = (2sqrt (5)) / 5

Kako najdete natančno vrednost tan [arc cos (-1/3)]?

Uporabljate trigonometrično identiteto tan (theta) = sqrt ((1 / cos ^ 2 (theta) -1)) Rezultat: tan [arccos (-1/3)] = barva (modra) (2sqrt (2)) dajanje arccos (-1/3) kot kota theta => arccos (-1/3) = theta => cos (theta) = - 1/3 To pomeni, da zdaj iščemo tan (theta). identiteta: cos ^ 2 (theta) + sin ^ 2 (theta) = 1 Delite vse obe strani s cos ^ 2 (theta), da imate, 1 + tan ^ 2 (theta) = 1 / cos ^ 2 (theta) = > tan ^ 2 (theta) = 1 / cos ^ 2 (theta) -1 => tan (theta) = sqrt ((1 / cos ^ 2 (theta) -1)) Spomnimo, prej smo rekli, da cos (theta) = -1 / 3 => tan (theta) = sqrt (1 / (- 1/3) ^ 2-1) = sqrt (1 / (1/9) -

Kako najdete natančno vrednost cos 36 ^ @ z uporabo formule vsote in razlike, dvojnega kota ali pol kota?

Tukaj ste že odgovorili. Najprej morate najti sin18 ^ @, za katere so podrobnosti na voljo tukaj. Nato lahko dobite cos36 ^ @, kot je prikazano tukaj.