Question

What is the domain of the inequality cos(2x) < 0 ?

a. x ∈ [0, 4)
b. x ∈ [4, 34)
c. x ∈ (0, 4) ∪ (4, 34)
d. x ∈ (0, 34)

Answer 1

The domain of the inequality cos(2x) < 0 is x ∈ (π, 3π) ∪ (5π, 7π). None of the answer is correct

Step-by-step explanation:

The domain of the inequality cos(2x) < 0 can be determined by finding the values of x for which the cosine of 2x is negative. To find these values, we need to consider the interval where the cosine function is negative. The cosine function is negative in the intervals (π/2, 3π/2) and (5π/2, 7π/2), and it repeats every 2π. Since we are dealing with 2x, the interval becomes (π, 3π) and (5π, 7π).

Therefore, the domain of the inequality is x ∈ (π, 3π) ∪ (5π, 7π).

None of the answer is correct