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# (Originais Teachy 2023) - Question Medium of Math

In a physics experiment, a student analyzes the trajectory of a particle and determines that its position with respect to time is given by the function f(t) = 2cos(t) - 3sin(t), where t is the time in seconds and f(t) is the position of the particle in meters. The student wants to know in which time intervals the particle is moving to the left. To do this, he needs to solve the following trigonometric inequality: 2cos(t) - 3sin(t) < 0. Solve this inequality for him.
a.
t ∈ (π/4, 3π/4)
b.
t ∈ (0, π/2)
c.
t ∈ (π/2, π)
d.
t ∈ (π, 3π/2)
e.
t ∈ (3π/2, 2π)

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