Final answer:
The question pertains to finding the arc length of a curve defined by parametric equations. Arc length on a circle is calculated using the radius and rotational angle, while for parametric curves it is done by integrating the speed function.
Step-by-step explanation:
The subject of Skill Builder 9.3 - Finding Arc Lengths of Curves Defined by Parametric Equations is to calculate the arc length of a curve using parametric equations for a specified interval. The arc length is the distance along a curved path, and it can be calculated by integrating the speed function obtained from the parametric equations of the curve. In the context of a circle, the arc length (As) is the product of the radius of curvature (r) and the rotational angle.
The process involves defining the radius of curvature, which is the radius of the circular path, and utilizing the rotational angle to determine the proportion of the circle's circumference that represents the arc. A full revolution of 360 degrees corresponds to a full circumference, which is 2π times the radius, while a partial rotation corresponds to a proportional part of the circumference.
When it comes to finding the arc length for parametric curves, the speed function is derived from the derivatives of the parametric equations. This function is then integrated over the given interval to find the total arc length of the curve.