The particle described by the function f(t) = cos(πt/4) is moving in the positive direction when the derivative f '(t) = -(π/4)sin(π(t)/4) is greater than zero. This occurs in the interval 4 < t < 8, as determined by analyzing the sine function's behavior. The critical points are derived from the inequality sin(πt/4) < 0, which indicates the particle's movement direction. The solution confirms that the particle is moving positively between these specific time values.
PREREQUISITESStudents studying calculus, particularly those focusing on motion analysis and trigonometric functions, as well as educators looking for examples of particle motion in mathematical contexts.
So after multiplying both sides by -4/π, you get sin(πt/4) < 0.Painguy said:Homework Statement
d) When is the particle moving in the positive direction?
[itex]f(t) = cos(πt/4), t ≤ 10[/itex]
Homework Equations
[itex]f '(t) = -(π/4)sin(π(t)/4)[/itex]
The Attempt at a Solution
[itex]0 < -(π/4)sin(π(t)/4)[/itex]
Painguy said:[itex](π(t)/4)>πn[/itex]
[itex]t>4n 0<=n<=2[/itex]
[itex]t>4 t>8[/itex]
The answer says 8>t>4
im probably skipping a simple step. wut do?