Kaj je tan (arcsin (12/13))?

Odgovor:

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

Pojasnilo:

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

To pomeni, da zdaj iščemo #color (rdeča) tantheta! #

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

Uporabi identiteto, # cos ^ 2theta + sin ^ 2theta = 1 #

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

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

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

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

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

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

Ne pozabite, kar smo klicali # theta # pravzaprav #arcsin (12/13) #

# => tan (arcsin (12/13)) = barva (modra) (12/5) #