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The length L of a line on a sphere of radius r between two points, specified in the spherical coordinate system as (r, 0a, Þa) and (r, Ob, Pb), is given by the integral L = r Sb /[o'($)]² + sin? Odø. What ordinary differential equation does the function 0(4) Фа that describes the shortest such line satisfy? Select one: O 1. sin² e = 0. Vcos?+sin² o O 2. /(@)² + sin? 0 + = 0. O 3. sin² 0 C, where C is some constant. V(os2+sin²o О 4. = 0. O 5. /(@)² + sin? 0 + C, where C is some constant. O6. V(@)2 + sin? 0 = C, where C is some constant.

The length L of a line on a sphere of radius r between two points, specified in the spherical coordinate system as (r, 0a, Þa) and (r, Ob, Pb), is given by the integral L = r Sb /[o'($)]² + sin? Odø. What ordinary differential equation does the function 0(4) Фа that describes the shortest such line satisfy? Select one: O 1. sin² e = 0. Vcos?+sin² o O 2. /(@)² + sin? 0 + = 0. O 3. sin² 0 C, where C is some constant. V(os2+sin²o О 4. = 0. O 5. /(@)² + sin? 0 + C, where C is some constant. O6. V(@)2 + sin? 0 = C, where C is some constant.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 74E
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The length L of a line on a sphere of radius r between two points, specified in the spherical coordinate system as (r, 0a, Pa) and (r, Ob, Pb), is given by the integral L = r rob V [O ($)]² + sin? Odø. What ordinary differential equation does the function 0(4) Фа that describes the shortest such line satisfy? Select one: sin?e 0. O 2. /(@)² + sin² 0 + = 0. О з. sin²e C, where C is some constant. О4. 0. O5. + sin? 0 + C. where C is some constant. O 6. V(@')2 + sin? 0 = C, where C is some constant.
Transcribed Image Text:The length L of a line on a sphere of radius r between two points, specified in the spherical coordinate system as (r, 0a, Pa) and (r, Ob, Pb), is given by the integral L = r rob V [O ($)]² + sin? Odø. What ordinary differential equation does the function 0(4) Фа that describes the shortest such line satisfy? Select one: sin?e 0. O 2. /(@)² + sin² 0 + = 0. О з. sin²e C, where C is some constant. О4. 0. O5. + sin? 0 + C. where C is some constant. O 6. V(@')2 + sin? 0 = C, where C is some constant.
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