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MathCalculus

Spherical Coordinate System: Convert the Point (-1, 2, 1)

Convert (-1, 2, 1) to spherical coordinates, resolve the quadrant, and round the angles to the nearest degree.

Question

Convert the Cartesian point (−1,2,1)(-1,2,1) into spherical coordinates (ρ,θ,ϕ)(\rho,\theta,\phi). Give both angles in degrees, rounding each to the nearest whole degree. Here θ\theta is the azimuth in the xyxy-plane and ϕ\phi is measured from the positive zz-axis.

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Evidence boundary

The point and nearest-integer degree requirement come from OpenStax Calculus Volume 3, Section 2.7, Exercise 390. This solution uses that section’s polar-angle convention. The radius is exact; the angle pair is rounded, so only the unrounded pair reproduces the Cartesian point exactly.