Question

seja x um angulo agudo tal que sen x = 4/5. Calcule o cos x,tg x,cotg x,sec x,cossec x

Answer 1

sen²x + cos²x = 1
cos²x = 1 - sen²x
cos²x = 1 - (4/5)²
cos²x = 1 - 20/25
cos²x = 25 - 20/25
cos x = √5/√25
cos x = √5/5

Tg x = sen x/cos x
Tg x = 4/5/√5/5
Tg x = 4/√5 (Racionalização )
Tg x = 4√5/5

Cotg x = cos x/sen x
Cotg x = √5/5/4/5
Cotg x = √5/4

sec x = 1/cos x
sec x = 1/√5/5
sec x = 5/√5
sec x = 5√5/5

cossec x = 1/sen x
cossec x = 1/4/5
cossec x = 5/4