Kdaj je sin (x) = frac {24cos (x) - sqrt {576cos ^ 2 (x) +448}} {14}?

Odgovor:

# x = 2pin + -sin ^ -1 (4/5) ……. ninZZ #

Pojasnilo:

#sin (x) = frac {24cos (x) - sqrt {576cos ^ 2 (x) +448}} {14} #

Preureditev dobimo, #.srt {576cos ^ 2 (x) +448} = 24cos (x) -14sin (x) #

Kvadriranje obeh strani in poenostavitev, dobimo

# 16 + 24sin (x) cos (x) = 7sin ^ 2 (x) #

# => 16 + 24sin (x) sqrt (1-sin ^ 2 (x)) = 7sin ^ 2 (x) #

# => 1-sin ^ 2 (x) = ((7sin ^ 2 (x) -16) / (24sin (x))) ^ 2 #

Če poenostavimo to, dobimo reducirno kvartično enačbo

# 625sin ^ 4 (x) -800sin ^ 2 (x) + 256 = 0 #

# => sin ^ 2 (x) = (800 + -sqrt ((800) ^ 2-4 * 625 * 256)) / (2 * 625) = 16/25 #

# => barva (modra) (x = 2pin + -sin ^ -1 (4/5)) #