Question

Seja a função ƒ, definida por ƒ(x) = sen x + cos x + cotg x + cossec x – tg x – sec x, ∀x ≠ 90°K e k∊ z. O valor de f (π/4) é. Os Cálculos são obrigatórios.

Answer 1

Explicação passo-a-passo:

f(x) = sen x + cos x + cotg x + cossec x – tg x – sec x

f(π/4) = sen (π/4) + cos (π/4) + cotg (π/4) + cossec (π/4) - tg (π/4) - sec (π/4)

Temos:

• sen (π/4) = √2/2

• cos (π/4) = √2/2

• cotg (π/4) = 1

• cossec (π/4) = √2

• tg (π/4) = 1

• sec (π/4) = √2

Assim:

f(π/4) = sen (π/4) + cos (π/4) + cotg (π/4) + cossec (π/4) - tg (π/4) - sec (π/4)

f(π/4) = √2/2 + √2/2 + 1 + √2 - 1 - √2

f(π/4) = 2√2/2 + 1 - 1 + √2 - √2

f(π/4) = √2