Question

va rog!!! 1,2 . . . . . . . . . .

Answer 1

Răspuns:

1.

Regula generala este că:

sin x ≥ 0, daca x ∈ [0+2kπ, π+2kπ]

sin x ≤ 0, daca x ∈ [π+2kπ, 2π+2kπ]

a) x = 12π / 7

12/7 ∈ [1, 2]  ⇒  x ∈ [π, 2π]  ⇒  sin x < 0

b) x = 37π / 36

37/36 ∈ [1, 2]  ⇒  x ∈ [π, 2π]  ⇒  sin x < 0

c) x = 30π / 31

30/31 ∈ [0, 1]  ⇒  x ∈ [0, π]  ⇒  sin x > 0

d) x = 5 ≈ 0,62π

⇒  x ∈ [0, π]  ⇒  sin x > 0

e) x = 29π / 18

29/18 ∈ [1, 2]  ⇒  x ∈ [π, 2π]  ⇒  sin x < 0

2.

Regula generala este că:

cos x ≥ 0, daca x ∈ [-π/2+2kπ, π/2+2kπ]

cos x ≤ 0, daca x ∈ [π/2+2kπ, 3π/2+2kπ]

a) x = 2π / 9

2/9 ∈ [-1/2, 1/2]  ⇒  x ∈ [-π/2, π/2]  ⇒  cos x > 0

b) x = 53π / 17 = (34+19)π / 17 = 2π + 19π/17

19/17 ∈ [1/2, 3/2]  ⇒  x ∈ [π/2, 3π/2]  ⇒  cos x < 0

c) x = 14π / 19

14/19 ∈ [1/2, 3/2]  ⇒  x ∈ [π/2, 3π/2]  ⇒  cos x < 0

d) x = 28π / 27

28/27 ∈ [1/2, 3/2]  ⇒  x ∈ [π/2, 3π/2]  ⇒  cos x < 0

e) x = 15π / 28

15/28 ∈ [1/2, 3/2]  ⇒  x ∈ [π/2, 3π/2]  ⇒  cos x < 0

Explicație pas cu pas: