EXAMPLE 4 Find a parametric representation for the sphere x2 + y2 + z2 = s². The sphere has a simple representation p = s in spherical coordinates, so let's choose the angles o and 0 in spherical coordinates as SOLUTION the parameters. Then, putting p = in the equations for y conversion from spherical to rectangular coordinates (these equations), we 0 = k obtain Video Example ) y = s sin(4) sin(0) z = X = as the parametric equations of the sphere. The corresponding vector equation is r(Ф, Ө) 3 We have 0 < P < n and 0 < 0 < 2n, so the parameter domain is the rectangle D = [0, x] × [0, 2n]. The grid curves with p constant are the circles with constant latitude (including the equators). The grid curves with O constant are the meridians (semi-circles), which connect the north and south poles (see the figure).

EXAMPLE 4 Find a parametric representation for the sphere x2 + y2 + z2 = s². The sphere has a simple representation p = s in spherical coordinates, so let's choose the angles o and 0 in spherical coordinates as SOLUTION the parameters. Then, putting p = in the equations for y conversion from spherical to rectangular coordinates (these equations), we 0 = k obtain Video Example ) y = s sin(4) sin(0) z = X = as the parametric equations of the sphere. The corresponding vector equation is r(Ф, Ө) 3 We have 0 < P < n and 0 < 0 < 2n, so the parameter domain is the rectangle D = [0, x] × [0, 2n]. The grid curves with p constant are the circles with constant latitude (including the equators). The grid curves with O constant are the meridians (semi-circles), which connect the north and south poles (see the figure).

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.6: Parametric Equations

Problem 5ECP: Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle...

See similar textbooks