A particle moves in the plane with velocity vector v(t)=⟨4cost,4sint⟩ for all real numbers t.
(a) Describe, without performing any numerical computations, how you can determine that the particle’s speed is the same for every value of t. Provide a clear verbal explanation referring to the structure of v(t).
(b) Explain which specific algebraic feature of the vector components guarantees the constancy of the speed.
(c) Interpret what a constant speed implies about the way the particle traverses its trajectory in the plane.