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To change Cartesian plane (x, y, z) to spherical polar coordinates (r, θ, φ)
  • a)
    x = r sin θ sin φ, y = r cosθ cos φ, z = r cos θ
  • b)
    x = r sin θ cos φ, y = r cos θ sin φ, z = r cos θ
  • c)
    x = r sin φ cos φ, y = r sin θ sin φ, z = r cos φ
  • d)
    r2 = x2 + y2 + z2 , tanθ = y/x,   φ = arccos(z/√(x2+y2+z2) )
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
To change Cartesian plane (x, y, z) to spherical polar coordinates (r,...
To convert a point from Cartesian coordinates to spherical coordinates, use equations 
 
r2 = x2 + y2 + z2 , tanθ = y/x,   φ = arccos(z/√(x2+y2+z2) )
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Most Upvoted Answer
To change Cartesian plane (x, y, z) to spherical polar coordinates (r,...
Θ, φ), we use the following formulas:

r = sqrt(x^2 + y^2 + z^2)
θ = arccos(z / r)
φ = atan2(y, x)

Here, r represents the radial distance from the origin to the point, θ represents the inclination angle measured from the positive z-axis, and φ represents the azimuthal angle measured from the positive x-axis.

To change spherical polar coordinates (r, θ, φ) to Cartesian coordinates (x, y, z), we use the following formulas:

x = r * sin(θ) * cos(φ)
y = r * sin(θ) * sin(φ)
z = r * cos(θ)

Here, sin and cos represent the sine and cosine functions, respectively.
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To change Cartesian plane (x, y, z) to spherical polar coordinates (r, θ, φ)a)x = r sin θsin φ, y = r cosθ cos φ, z = r cos θb)x = r sin θ cos φ, y = r cos θ sin φ, z = r cosθc)x = r sin φ cos φ, y = r sin θ sin φ, z = r cos φd)r2= x2+ y2+ z2, tanθ = y/x, φ = arccos(z/√(x2+y2+z2) )Correct answer is option 'D'. Can you explain this answer?
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To change Cartesian plane (x, y, z) to spherical polar coordinates (r, θ, φ)a)x = r sin θsin φ, y = r cosθ cos φ, z = r cos θb)x = r sin θ cos φ, y = r cos θ sin φ, z = r cosθc)x = r sin φ cos φ, y = r sin θ sin φ, z = r cos φd)r2= x2+ y2+ z2, tanθ = y/x, φ = arccos(z/√(x2+y2+z2) )Correct answer is option 'D'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about To change Cartesian plane (x, y, z) to spherical polar coordinates (r, θ, φ)a)x = r sin θsin φ, y = r cosθ cos φ, z = r cos θb)x = r sin θ cos φ, y = r cos θ sin φ, z = r cosθc)x = r sin φ cos φ, y = r sin θ sin φ, z = r cos φd)r2= x2+ y2+ z2, tanθ = y/x, φ = arccos(z/√(x2+y2+z2) )Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for To change Cartesian plane (x, y, z) to spherical polar coordinates (r, θ, φ)a)x = r sin θsin φ, y = r cosθ cos φ, z = r cos θb)x = r sin θ cos φ, y = r cos θ sin φ, z = r cosθc)x = r sin φ cos φ, y = r sin θ sin φ, z = r cos φd)r2= x2+ y2+ z2, tanθ = y/x, φ = arccos(z/√(x2+y2+z2) )Correct answer is option 'D'. Can you explain this answer?.
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