Final answer:
The student's question pertains to converting a point from spherical to Cartesian coordinates, specifically finding the x-coordinate in the Cartesian system using the formula x = r sin(ϴ) cos(φ).
Step-by-step explanation:
The student is asking about the relationship between spherical and rectangular (Cartesian) coordinate systems, and how to find the Cartesian coordinate vector of a point given in spherical coordinates. The spherical coordinates (r, ϴ, φ) consist of a radial distance r, a polar angle ϴ (theta), and an azimuthal angle φ (phi). The student's question specifically concerns the x-coordinate vector in the Cartesian system, which can be found using the transformation equations:
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- x = r sin(ϴ) cos(φ)
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- y = r sin(ϴ) sin(φ)
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- z = r cos(ϴ)
So the x-coordinate of a point in a Cartesian coordinate system, when given its spherical coordinates, is obtained by the formula x = r sin(ϴ) cos(φ).