Let o(0,ø) = (cos 0 sin ø, sin 0 sin ó, cos 6) be a parametrization of the unit sphere. Show that the curve defined for 0 < t < by 1(4) = o (In cot( -)5-1), makes a constant angle with the parallels (ø = constant) on the unit sphere.

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A: the formula used to find the radius of curvature is  K=|y''|1+y'23/2                       (1)R=1K

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Q: 1 Evaluate f - dz over the unit circle in counter-clockwise direction using the parametriza- tions

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A: The given curve is the intersection of paraboloid z = x2+y2 and ellipsoid 3x2+2y2+6z2 = 29.

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Q: 8. Find a plane curve a(s) endowed with a unit-speed prametrization by S E (-∞, 0) such that its…

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A: The solution is following.

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Q: Find the Torsion along the curve: X = (t-sin t)ê +(1- cos t)ê, +tê,. %3D

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Q: 13. Find the point on the curve 7(t) = (2 sin t, 2 cos t, t), 0<ts 7, where the tangent line is…

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Q: Consider the parametric curve C given by X= St. y = 5 sin²t where te [0.2] (₁) Determine the values…

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Q: Consider the parametric curve x(t) = a cos t, y(t) = b sin t, 0 <t<n for a # 0, b # 0 a) Sketch and…

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Q: Please solve

A: Parametrization of tangent lines is given by

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Q: ..... The area of the surface generated by revolving the curve x = 1 cos (2t), y = 7+ -sin (2t) on…

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A: Given that: z=x2-2y2      and point is:   (1, 1, 1)

Q: x = 1+ vt, y = et X =1+1 Y. %3D

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Q: Find a plane curve a(s) endowed with a unit-speed prametrization by SE (-0, 0) such that its signed…

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Q: Suppose F(2, y) = -y sin(æ)i + cos(2)j. (a) Find a vector parametric equation for the parabola y =…

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Q: Consider the given curve: R(f) = (2 cos f, 12f +3,-2 sin f) Reparametrize the curve using arclength…

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Q: Let C be the closed curve starting at (0, 1) traveling along the parabola y = (x – 1)? up to the…

A: Using Green's Theorem we solve the above question.