Question

8- Se sec x = V2, calcule a cossec x.
9- Sabendo que tg x = 3/5 com x E 3° quadrante, determine o valor da expressão y = cos x - sen x.​

Answer 1

Resposta:

Explicação passo-a-passo:

8- Se sec x = V2, calcule a cossec x.

sec x = 1/cos

√2 = 1/cos

cos.√2 = 1

cos = 1/√2 . √2/√2

cos = √2/2

sen^2 x + cos^2 x = 1

sen^2 x + (√2/2)^2 = 1

sen^2 x + 2/4 (:2)/(:2) = 1

sen^2 x + 1/2 = 1

sen^2 x = 1 - 1/2

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

sen^2 x = 1/2

sen x = √1/2

sen x = 1/√2 . √2/√2

sen x = √2/2

cossec x = 1/sen

Cossec x = 1 / √2/2

Cossec x = 1 . 2/√2

Cossec x = 2/√2 .√2/√2

Cossec x = 2√2/2

Cossec x = √2

9- Sabendo que tg x = 3/5 com x E 3° quadrante, determine o valor da expressão y = cos x - sen x.​

Tg x = 3/5

3° quadrante

Sen x = (-)

Cos x = (-)

tg² (x) + 1 = sec² (x)

(3/5)^2 + 1 = sec² (x)

9/25 + 1 = sec² (x)

(9+25)/25 = sec² (x)

34/25 = sec² (x)

sec² (x) = 34/25

sec (x) = √(34/25)

sec x = √34 /5

Sec x = 1/cos x

√34 /5 = 1/ cos x

Cos x .√34 = 1.5

Cos x = 5/√34 . √34/√34

Cos x = 5√34/34

3° quadrante

Cos x = - 5√34/34

Tg x = 3/5

Tg x = sen x / cos x

3/5 = sen x / 5√34/34

3/5 = sen x . 34 /5√34

3.5√34 = sen x . 34.5

3√34 = 34. Sen x

3√34/34 = sen x

sen x = 3√34/34

3° Q: (-)

Sen x = - 3√34/34

Sendo:

Cos x = - 5√34/34

Sen x = - 3√34/34

y = cos x - sen x

y = - 5√34/34 - ( - 3√34/34)

y = - 5√34/34 + 3√34/34

y = - 2√34/34 (:2)/(:2)

y = - √34/17

R.: y = - √34/17