Question

Dado o sen0=4/5, calcule o cos0, tg0, cotg0, sec0 e cossec0.

Answer 1

sen Θ = 4/5
sen = C.O. / Hip
C.O. = 4
Hip = 5

sen² Θ + cos² Θ = 1
(4/5)² + cos²  = 1
16/25 + cos² = 1
cos² = 1 - 16/25
cos² = 25 - 16/25
cos² = 9/25
cos = √9/25
cos = 3/5

tg Θ = sen Θ / cos Θ
tg Θ = 4/5 / 3/5
tg Θ = 4/5 * 5/3
tg Θ = 4/3

cotg Θ = 1/tgΘ 
cotg Θ = 1 /4/3
cotg Θ = 1 * 3/4
cotg Θ = 3/4

sec Θ = 1 / cosΘ
sec Θ = 1 / 3/5
sec Θ = 1 * 5/3
sec Θ = 5/3

cossec Θ = 1 / sen Θ
cossec Θ = 1 / 4/5
cossec Θ = 1 / 4/5
cossec Θ = 1 * 5/4
cossec Θ = 5/4