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Engineering Calculus Notes 25

# Engineering Calculus Notes 25 - spherical coordinates...

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1.1. LOCATING POINTS IN SPACE 13 (e) x = 3, y = 1, z = 1 4. Given the spherical coordinates of the point, Fnd its rectangular coordinates: (a) ρ = 2 , θ = π 3 , φ = π 2 (b) ρ = 1 , θ = π 4 , φ = 2 π 3 (c) ρ = 2 , θ = 2 π 3 , φ = π 4 (d) ρ = 1 , θ = 4 π 3 , φ = π 3 5. What is the geometric meaning of each transformation (described in cylindrical coordinates) below? (a) ( r,θ,z ) ( r,θ, z ) (b) ( r,θ,z ) ( r,θ + π,z ) (c) ( r,θ,z ) ( r,θ π 4 ,z ) 6. Describe the locus of each equation (in cylindrical coordinates) below: (a) r = 1 (b) θ = π 3 (c) z = 1 7. What is the geometric meaning of each transformation (described in
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Unformatted text preview: spherical coordinates) below? (a) ( ρ,θ,φ ) → ( ρ,θ + π,φ ) (b) ( ρ,θ,φ ) → ( ρ,θ,π − φ ) (c) ( ρ,θ,φ ) → (2 ρ,θ + π 2 ,φ ) 8. Describe the locus of each equation (in spherical coordinates) below: (a) ρ = 1 (b) θ = π 3 (c) φ = π 3 9. Express the plane z = x in terms of (a) cylindrical and (b) spherical coordinates....
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