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Show that the following trajectory lies on a sphere centered at the origin, and find the radius of the sphere. 8 sin 2t 8 cos 2t 8 sin 6t r(t)= 0≤t≤2 1 + sin 26t 1 + sin 26t 1 + sin 26t The trajectory described by r(t) lies on a sphere centered at the origin if the magnitude of r(t) equals a constant for 0 st≤2, which implies that the magnitude squared also equals a constant. Start by setting up the expression for the magnitude squared of r(t). 8 sin 2t = 1 + sin 6t 2 8 cos 2t 1 + sin 6t 8 sin 6t + 1 + sin 26t 2 2 2 +V +V (Type the terms of your expression in the same order as they appear in the original expression.) Next expand each of the squared terms and factor out a constant. Tr 2 = = 64 sin 22t+64 cos 22t+64 sin 26t g² 2 1 + sin "6t 1 + sin 26t sin 22t+ cos 22t+ sin 26t (Simplify your answer.) 1 + sin 26t Expand and combine fractions. Factor.

Show that the following trajectory lies on a sphere centered at the origin, and find the radius of the sphere. 8 sin 2t 8 cos 2t 8 sin 6t r(t)= 0≤t≤2 1 + sin 26t 1 + sin 26t 1 + sin 26t The trajectory described by r(t) lies on a sphere centered at the origin if the magnitude of r(t) equals a constant for 0 st≤2, which implies that the magnitude squared also equals a constant. Start by setting up the expression for the magnitude squared of r(t). 8 sin 2t = 1 + sin 6t 2 8 cos 2t 1 + sin 6t 8 sin 6t + 1 + sin 26t 2 2 2 +V +V (Type the terms of your expression in the same order as they appear in the original expression.) Next expand each of the squared terms and factor out a constant. Tr 2 = = 64 sin 22t+64 cos 22t+64 sin 26t g² 2 1 + sin "6t 1 + sin 26t sin 22t+ cos 22t+ sin 26t (Simplify your answer.) 1 + sin 26t Expand and combine fractions. Factor.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 39E
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Show that the following trajectory lies on a sphere centered at the origin, and find the radius of the sphere. 8 sin 2t 8 cos 2t 8 sin 6t r(t)= 0≤t≤2 1 + sin 26t 1 + sin 26t 1 + sin 26t The trajectory described by r(t) lies on a sphere centered at the origin if the magnitude of r(t) equals a constant for 0 st≤2, which implies that the magnitude squared also equals a constant. Start by setting up the expression for the magnitude squared of r(t). 8 sin 2t = 1 + sin 6t 2 8 cos 2t 1 + sin 6t 8 sin 6t + 1 + sin 26t 2 2 2 +V +V (Type the terms of your expression in the same order as they appear in the original expression.) Next expand each of the squared terms and factor out a constant. Tr 2 = = 64 sin 22t+64 cos 22t+64 sin 26t g² 2 1 + sin "6t 1 + sin 26t sin 22t+ cos 22t+ sin 26t (Simplify your answer.) 1 + sin 26t Expand and combine fractions. Factor.
Transcribed Image Text:Show that the following trajectory lies on a sphere centered at the origin, and find the radius of the sphere. 8 sin 2t 8 cos 2t 8 sin 6t r(t)= 0≤t≤2 1 + sin 26t 1 + sin 26t 1 + sin 26t The trajectory described by r(t) lies on a sphere centered at the origin if the magnitude of r(t) equals a constant for 0 st≤2, which implies that the magnitude squared also equals a constant. Start by setting up the expression for the magnitude squared of r(t). 8 sin 2t = 1 + sin 6t 2 8 cos 2t 1 + sin 6t 8 sin 6t + 1 + sin 26t 2 2 2 +V +V (Type the terms of your expression in the same order as they appear in the original expression.) Next expand each of the squared terms and factor out a constant. Tr 2 = = 64 sin 22t+64 cos 22t+64 sin 26t g² 2 1 + sin "6t 1 + sin 26t sin 22t+ cos 22t+ sin 26t (Simplify your answer.) 1 + sin 26t Expand and combine fractions. Factor.
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