Question

1 - Dado cos x = - 1/2, com, <x<x, calcule a cotg x.
2 - Dado sen x = 1/3, determinar a tg x.
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Answer 1

Resposta:

Explicação passo-a-passo:

sen^2 x + cos^2 x = 1

cos x = - 1/2

Sen^2 x + (-1/2)^2 = 1

sen^2 x + 1/4 = 1

sen^2 x = 1 - 1/4

sen ^2 x = (4-1)/4

sen ^2 x = 3/4

sen x = √(3/4)

sen x = √3/2

cotg = 1/tg

cotg = cos x/sen x

cotg = - 1/2 : √3/2

cotg = - 1/2 . 2/√3

cotg = 2/2 . (-1/√3)

cotg = -1/√3 .√3//√3

cotg x = - √3/3

2)

2 - Dado sen x = 1/3, determinar a tg x.

Sen^2 x + cos^2 x = 1

(1/3)^2 + cos^2 x = 1

1/9 + cos^2 x = 1

cos ^2 x = 1 - 1/9

cos^2 x = (9-1)/9

cos^2 x = 8/9

cos x = √8/√9

cos x = √4.√2/3

cos x = 2√2/3

Tg x = sen x/ cos x

Tg x = 1/3 : 2√2/3

Tg x = 1/3 . 3/2√2

Tg x = 3/3 . 1/2√2

Tg x = 1/2√2 . √2/√2

Tg x = √2/2.2

Tg x = √2/4