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

Odgovor:

Uporabljate trigonometrično identiteto #tan (theta) = sqrt ((1 / cos ^ 2 (theta) -1)) #

Rezultat: #tan arccos (-1/3) = barva (modra) (2sqrt (2)) #

Pojasnilo:

Začnite z najemom #arccos (-1/3) # biti kot kot # theta #

# => arccos (-1/3) = theta #

# => cos (theta) = - 1/3 #

To pomeni, da zdaj iščemo #tan (theta) #

Nato uporabite identiteto: # cos ^ 2 (theta) + sin ^ 2 (theta) = 1 #

Razdelite vse na obe strani # cos ^ 2 (theta) # imeti, # 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 se, da smo prej rekli #cos (theta) = - 1/3 #

# => tan (theta) = sqrt (1 / (- 1/3) ^ 2-1) = sqrt (1 / (1/9) -1) = sqrt (9-1) = sqrt (8) = sqrt (4xx2) = sqrt (4) xxsqrt (2) = barva (modra) (2sqrt (2)) #