Question

Is the curve r(t) = (cost, sint) parametrized by its arc length? Explain.

Choose the correct answer below.
A. Yes. The curve is parametrized by its arc length because [v(t) = t for all t. Thus, v(t) = 1 for t = 1.
B. Yes. The curve is parametrized by its arc length because v(t) = 1 for all t
C. No. The curve is not parametrized by its arc length because [v(t) = r(t) for all t
D. No. The curve is not parametrized by its arc length because [v(t) = cost-sint

Answer 1

No, the curve is not parametrized by its arc length because the function v(t) is not equal to 1 for all t.

Step-by-step explanation:

No. The curve is not parametrized by its arc length because v(t) = cos(t) - sin(t), which is not equal to 1 for all t. An arc length parametrization would have v(t) equal to 1 for all t. Therefore, the correct answer is D. The curve is not parametrized by its arc length because v(t) = cos(t) - sin(t).