(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

r(t) = [cos(t^3)sin(t), sin(t)sin(t^3), cos(t)], where t is an element of (0,2pi).

Show that the graph of this function is on the surface of a sphere. Then find it's radius.

2. Relevant equations

T(t) =r'(t)/norm[r'(t)]

equation for a sphere in 3-space: r^2=x^2+y^2+z^2

3. The attempt at a solution

My thought is, a tangent vector must lie on the surface of this function (which is a sphere), and therefore the tangent vector at some point (t) would be sufficient proof. But that seems too easy.

Secondly, to find the radius of a sphere, set up the parametric equations in the form of x= cos(t^3)sin(t), y = sin(t^3)sin(t), z = cos(t), in the form of the equation for a sphere:

(cos(t^3)sin(t))^2 + (sin(t^3)sin(t))^2 + (cos(t))^2 = r^2

then substitute one of the elements to find the radius squared?

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# Homework Help: Show that the vector value function is on the surface of a sphere

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