MATH 2531: SECTION 13.3 WRITTEN ASSIGNMENT Find the arc length parameterization of the curve r(t) = 4 cos(t)i + 4 sin(t)j + 3th by completing the following parts. 1. Find the derivative v(t) for the curve r(t). 2. Using your answer to #1, find the magnitude v(t) . Use the Pythagorean identity to simplify your answer. 3. Using your answer to #2 and the arc length parameter formula on p. 782, using to = 0 as a basepoint, find the arc length parameter s(t) for the curve.Chapter 13 Vector-Valued Functions and Motion in Space 782 Chapter 13 Vector-Valued Functions and Motion in Space Arc Length Formula (2) EXAMPLE 1 A glider is soaring upward along the helix r(1) = (cos ni + (sin n)j + tk. How long is the glider's path from ? = 0 to f = 2n? Solution The path segment during this time corresponds to one full turn of the helix Figure 13.13). The length of this portion of the curve is 1 = 20 L - J Wvla - Vi-sino + (cos of + (1)'d) Vidi = 2T V2 units of length. (1, 0. 0) =0 This is V2 times the circumference of the circle in the xy-plane over which the helix stands. FIGURE 13.13 The helix in Example 1. If we choose a base point P(t) on a smooth curve Cparametrizatione of r(n) = (cos ni + (sin nj + rk. determines a point P(t) = (x(t), y(1), z()) on C and a "directed distance" measured along C from the base point (Figure 13.14). This is the are length function we defined in Section 11.2 for plane curves that have no z-component. If f > bo, s() is the distance along the curve from P(4) to P(). If /