Čo je opálenie (arcsin (12/13))?

odpoveď:

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

vysvetlenie:

nechať# "" theta = arcsin (12/13) #

To znamená, že teraz hľadáme #COLOR (red) tantheta #!

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

Použiť identitu, # 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) #

Obnoviť: # 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 #

Pripomeňme si, čo sme volali # # Theta bol vlastne #arcsin (12/13) #

# => tan (arcsin (12/13)) = farba (modrá) (12/5) #