Imagine a pole of unit radius stuck in the ground at the origin. A thin string is wrapped to the left many times around the pole (clockwise direction as seen from above) and you are holding it tightly against the pole at (1,0).

If you hold the string tightly, you can unwind it by walking in a spiral to the right (counterclockwise.)

Task 1: Find parametric equations for your path.

Task 2: If you adjust your speed so the string unwinds at a constant rate of 1 revolution every 2π seconds and graph your position over time, formulate the x- and y-intercepts of this graph.