WH 06 Parametric Equations Updated automatically every 5 minutes Unwindin . Strin . In this problem, we will be thinking about a parametric curve and imagining a string unwound from that curve. We are trying to think about the path traced out by the end of the string as if there was a pen on that string. Here is an animation of this happening for a few different curves. The red curve is the one from which the string is unwound, the black dotted line represents the string, and the green curve represents the curve traced out by the end of that string. This green traced curve is the one we'll be interested in describing. Preliminary problems . Draw a line with positive slope m. Label the acute angle this line makes with the x-axis as theta. Find a relationship between m and theta. . Draw a line with negative slope m. Label the acute angle this makes with the x-axis as theta. Show that the same relationship from above holds. Curve 1 Consider the curve described by the parametric equations W) = "V3 and W) = 1'13. (this is the middle animation, by the way) . Find the arc length along this curve from the origin (t=0) to point T_O (t: t_0), some arbitrary point. . To make the rest of the computations easier, assume that the string initially extends a distance of 1/3 beyond the origin. What is the length of the string from the point T_O to the point P? . At T_0, the string is tangent to the curve. Find the slope of this tangent line