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## Homework Statement

**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.

## Homework Equations

**T**(t) =

**r**'(t)/norm[

**r**'(t)]

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

## 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?