Question

Se o sen x = 1/4, então o cos x, tg x, sec x e cossec x são respectivamente: 


a) √15/4 , √15/15 , 4√15/15 e 1

b) 3√15/4 , √15/15 , 4√15/15 e 1

c) √15/4 , √15/15 , 2√15/15 e 4

d) √15/4 , √15/15 , 4√15/15 e 4

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Answer 1

Resposta:

Alternativa D.

Explicação passo-a-passo:

sen² x + cos² x = 1

(1/4)² + cos² x = 1

1/16 + cos² x = 1

cos² x = 1 - 1/16

cos²x = 15/16

cos x = √(15/16)

cos x = √15/4

tg x = sen x ÷ cos x

tg x = 1/4 ÷ √15/4

tg x = 1/4 × 4/√15

tg x = 1/√15 × √15/√15

tg x = √15/15

sec x = 1 ÷ cos x

sec x = 1 ÷ √15/4

sec x = 1 × 4/√15

sec x = 4/√15 × √15/√15

sec x = 4√15/15

cossec x = 1 ÷ sen x

cossec x = 1 ÷ 1/4

cossec x = 1 × 4

cossec x = 4