Identify the geometric object that is represented by parametric equations $\mathbf { r } ( t , s ) = \langle 3 \sin s \cos t , 3 \sin s \sin t , 3 \cos s \rangle$ .
A)A plane
B)A cone
C)A straight line
D)A circular cylinder
E)A circle
F)A circular disk
G)A helix
H)A sphere

Question

Quizplus · Accepted Answer

The given parametric equations represent a sphere of radius 3. The parameters $s$ and $t$ can be seen as spherical coordinates, where $s$ represents the polar angle and $t$ the azimuthal angle. The equations describe all points in space at a fixed distance (3) from the origin, which is the definition of a sphere.

Identify the Geometric Object That Is Represented by Parametric Equations r(t,s)=⟨3sin⁡scos⁡t,3sin⁡ssin⁡t,3cos⁡s⟩\mathbf { r } ( t , s ) = \langle 3 \sin s \cos t , 3 \sin s \sin t , 3 \cos s \rangler(t,s)=⟨3sinscost,3sinssint,3coss⟩

Identify the Geometric Object That Is Represented by Parametric Equations $\mathbf { r } ( t , s ) = \langle 3 \sin s \cos t , 3 \sin s \sin t , 3 \cos s \rangle$