The position vector of a particle moving in the x-y plane is

Question

The position vector of a particle moving in the x-y plane is  in the interval [0, 2π). For what value(s) of t does the path of the particle have a horizontal tangent? (5 points)

answer choices

	0, π
	None of these

Answer 1

Given the position vector , the vector tangent to the path is given by the derivative with respect to the parameter "t" of the position vector: (-2sin t, 4cost). The tangent vector is horizontal when 4*cos(t) = 0, i.e. when t = pi/2 and 3/2*pi.