Question

Dados sen x = - V7/4, x E 3° quadrante, determine cotg x.​

Answer 1

sen x = - V7/4 ==> cossecx = -4/√7

1 +cotg²x = cossec²x

cotg²x = cossec²x - 1 ==> 1=7/7

cotg²x = 16/7 - 7/7

cotg²x = 9/7

cotg x = √9/7 = 3/√7 = 3√7 /7 ✓

Answer 2

Resposta:

Cotg x = 3√7/7

Explicação passo-a-passo:

sen x = - V7/4, x E 3° quadrante, determine cotg x.​

3°Q

sen x = (-)

Cos x = (-)

Senx = -√7/4

sen ^2 x + cos^2 x = 1

(-√7/4)^2 + cos^2 x = 1

7/16 + cos ^2 x = 1

cos^2 x = 1 - 7/16

cos^2x = (16-7)/16

cos^2 x = 9/16

Cos x = √(9/16)

cos x = 3/4

3°Q

Cos x = (-)

cos x = - 3/4

Cotg x = cos x/sen x

Cotg x = - 3/4 : (-√7/4)

Cotg x = 3/4 . 4/√7

Cotg x = 4/4 . 3/√7

Cotg x = 3/√7 . √7/√7

Cotg x = 3√7/7