Question

Se cos x = - V5/5 . II <x< 3II/ 2, calcule demais funções circulares

Answer 1

Resposta:

sen x = 2√5/5

Tg x = 2

Cotg x = 1/2

Sec x = - √5

Cossec x = - √5/2

Explicação passo-a-passo:

Se cos x = - V5/5 .

π <x< 3π/ 2, calcule demais funções circulares

Entre 180° e 270°= 3°Quadrante

cos x = (-)

sen x = (-)

Cos x = - √5/5

cos^2 x + sen^2 x = 1

(-√5/5)^2 + sen^2 x = 1

5/25 (:5)/(:5) + sen^2 x = 1

1/5 + sen^2x = 1

sen^2 x = 1 - 1/5

sen^2 x = (5 - 1)/5

sen^2 x = 4/5

sen x = √4/√5

sen x = 2/√5 . √5/√5

sen x = 2√5/5

3° q

Sen x = - 2√5/5

Tg x = sen x/cos x

Tg x = - 2√5/5 : (-√5/5)

Tg x = 2√5/5 . 5/√5

Tg x = 5.2√5/ 5.√5

Tg x = 2

Cotg x = 1/tg x

Cotg x = 1/2

Sec x = 1/cos x

Sec x = 1 : (-√5/5)

Sec x = 1 . (-5/√5)

Sec x = - 5/√5 .√5/√5

Sec x = - 5√5/5

Sec x = - √5

Cossec x = 1/sen x

Cossec x = 1 : (-2√5/5)

Cossec x = 1 . (- 5/2√5)

Cossec x = - 5/2√5 . √5/√5

Cossec x = - 5√5/2√5.√5

Cossec x = - 5√5/2.5

Cossec x = - 5√5/10 (:5)/(:5)

Cossec x = - √5/2