Question

Determine sen x + cos x, sendo sec x = - 3/5 , com II/2 . <x<II.​

Answer 1

secx= -5/3 (correto) ===> cosx = -3/5

senx=√1-cos²x=√1-(9/25)=√16/25=4/5

=> sen x + cos x = 4/5 - 3/5 = 1/5 ✓

Answer 2

Resposta:

1/5

Explicação passo-a-passo:

Sec x = - 5/3

sen x + cos x, sendo

sec x = - 5/3 , com π/2 < x < π

Entre: π/2 e π = 2° Quadrante

sen x = (+)

cos x = (-)

Sec x = - 5/3

Sec x = 1/cos x

- 5/3 = 1/ cos x

- 5 Cos x = 3 (-1)

5 cos x = - 3

Cos x = - 3/5

Cos^2 x + sen^2 x = 1

(-3/5)^2 + sen^2 x = 1

9/25 + sen^2 x = 1

sen^2 x = 1 - 9/25

sen^2 x = (25-9)/25

sen^2 x = 16/25

sen x = √(16/25)

sen x = 4/5

= Sen x + cos x

= 4/5 - 3/5

= 1/5