Question

Reparametrize the curve with respect to arc length measured from the point where t = 0 in the direction of increasing t. (Enter your answer in terms of s.)

Answer 1

To reparametrize a curve with respect to arc length measured from the point where t = 0, we need to find a new parameterization using the arc length, s. The relationship between arc length and angle is given by: Δθ = s/r, where Δθ is the change in angle, s is the arc length, and r is the radius of curvature. Therefore, to reparametrize the curve with respect to arc length, we can use the equation: s = rΔθ.

Step-by-step explanation:

To reparametrize a curve with respect to arc length measured from the point where t = 0, we need to find a new parameterization using the arc length, s.

The relationship between arc length and angle is given by: Δθ = s/r, where Δθ is the change in angle, s is the arc length, and r is the radius of curvature.

Therefore, to reparametrize the curve with respect to arc length, we can use the equation: s = rΔθ.