Što je tan (arcsin (12/13))?

Što je tan (arcsin (12/13))?
Anonim

Odgovor:

#tan (arcsin (12/13)) = 12/5 #

Obrazloženje:

pustiti# "" theta = arcsin (12/13) #

To znači da sada tražimo #COLOR (crvena) tantheta! #

# => Sin (theta) = 12/13 #

Koristi identitet, # Cos ^ 2 theta + grijeh ^ 2 theta = 1 #

# => (Cos ^ 2 theta + sin ^ 2 theta) / cos ^ 2 theta = 1 / cos ^ 2 theta #

# => 1 + sin ^ 2 theta / cos ^ 2 theta = 1 / cos ^ 2 theta #

# => 1 + tan ^ 2 theta = 1 / cos ^ 2 theta #

# => tantheta = sqrt (1 / cos ^ 2 (theta) -1) #

Podsjetimo: # cos ^ 2theta = 1-sin ^ 2theta #

# => Tantheta = sqrt (1 / (1-sin ^ 2 theta) -1) #

# => Tantheta = sqrt (1 / (1- (12/13) ^ 2), 1) #

# => Tantheta = sqrt (169 / (169-144) -1 #

# => Tantheta = sqrt (169 / 25-1) #

# => tantheta = sqrt (144/5) = 12/5 #

ZAPAMTITE ono što smo zvali # Teta # zapravo je #arcsin (12/13) *

# => tan (arcsin (12/13)) = boja (plava) (12/5) #