Question

Sendo cos x = - 2V2/3, com II/2 <x<II, calcule tg x e cotg x.​

Answer 1

Resposta:

Tg x = - √2/4

Cotg x = - 2√2

Explicação passo-a-passo:

cos x = - 2V2/3, com II/2 <x<II, calcule tg x e cotg x.​

π/2 e π = 2° Q

Sen x = (+)

Cos x = (-)

Sen^2 x + cos^2 x = 1

Sen^2 x + (- 2V2/3)^2 = 1

Sen^2 x + (4.2/9) = 1

Sen^2 x + 8/9 = 1

Sen^2 x = 1 - 8/9

Sen^2 x = (9-8)/9

sen^2 x = 1/9

sen x = √(1/9)

sen x = 1/3

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 . 1/2√2 . √2/√2

Tg x = - 1 . √2/(2√2.√2)

Tg x = - √2/(2.2)

Tg x = - √2/4

Cotg x = 1/ tg x

Cotg x = 1 / (-√2/4)

Cotg x = - 4/√2 . √2/√2

Cotg x = - 4√2/2

Cotg x = - 2√2