calculus question

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 vertical tangent?

	0, π
	None of these

Answer 1

The velocity vector is tangent to the path of the particle. The velocity vector is the time derivative of the position vector. d/dt<2cost, 4sint> = <-2sint, 4cost>.

When does the velocity vector point vertically? This happens when the x component of the velocity vector is zero.

-2sint = 0 when t = 0, π.