1 Coordinates We now tabulate for reference the same kind of information for spherical coordinates r, 0, þ. These coordinates are shown in Figure A.6-1b. They are related to the Cartesian co- ordinates by |x =r sin 0 cos y =r sin 0 sin o z =r cos 0 (A.6-19) (A.6-20) (A.6-21) r = +V* + y} + z? 0 = arctan(Vx² + y²/z) $ = arctan(y/x) (A.6-22) (A.6-23) (A.6-24) For the spherical coordinates we have the following relations for the derivative operators: Cos 0 cos o sin o = (sin 0 cos 6) + + (A.6-25) dx dr r sin 0) ap Cos 0 sin ø Cos o = (sin 0 sin ¢) ду ar r sin 0) ap (A.6-26) sin 0 = (cos 0) dz + (0) дф (A.6-27) dr
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How do we go from A6.22-24 to expressions in A.25-27? Can you please show me step by step derivation? Thanks
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