Let 3 x = cos' t, y = sin³ t, z = 7; 0 < t < r. Find the arc length of the parametric curve.

Q: Find the equation of the curve whose parametric equations are x = 1+ 4 cos 8, y = 2 + 3 sin 0, 0 €…

A: We have to find the equation of curves whose parametric equation is given by

Q: Parameterize the curve r(t) = (2+ cos 3t, 3 – sin 3t, 4t) using arc length, s, as a parameter. Use t…

A: Given the curve rt=2+cos3t, 3-sin3t, 4t---1. Differentiating, we get vt=r't=-3sin3t,…

Q: SKet the cerve r²= 29° cOS 20

A:

Q: Without using a graphing utility, show that the parametric curve r(t) = (3t cos(3t), 3t sin(3t), 3t)…

A:

Q: Find the slope of the tangent line to the polar curve 7 = 1-sin 40 at 0= 04 0- 12/12 O 5√3+4 1-4√3

A:

Q: Write an equation of the tangent line to the parametric equation at the given value of t. Please…

A:

Q: A curve is defined by the parametric equations T = sin t, y = 1 – cos t, 0<t< 27.

A: Given parametric equations is x = sin t; y = 1 - cos t, 0 ≤t≤2π b) Eliminate t and determine what…