Final answer:
To convert spherical coordinates to rectangular coordinates, use r, φ, and θ to compute the x, y, and z components using the conversion formula. For the provided spherical coordinates (8, 6, 4), substitute these into x = r × sin(φ) × cos(θ), y = r × sin(φ) × sin(θ), and z = r × cos(φ) to obtain the rectangular coordinates.
Step-by-step explanation:
To convert the point from spherical coordinates (r, φ, θ) to rectangular coordinates (x, y, z), we can use the following relationships based on the spherical to rectangular coordinate conversions:
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- x = r × sin(φ) × cos(θ)
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- y = r × sin(φ) × sin(θ)
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- z = r × cos(φ)
In this case, the spherical coordinates given are r=8, φ=6, and θ=4. Assuming that φ and θ are measured in radians, we substitute these values into the equations:
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- x = 8 × sin(6) × cos(4)
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- y = 8 × sin(6) × sin(4)
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- z = 8 × cos(6)
These calculations will give the Cartesian (rectangular) coordinates of the point originally given in spherical coordinates.