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Spherical coordinates

Spherical coordinates. z. y. x. Spherical coordinates. z. y. x. P(x,y,z). Spherical coordinates. z. y. x. P(x,y,z). P’(x,y,0). Spherical coordinates. z. y. x. P(x,y,z). x. y. P’(x,y,0). Spherical coordinates. z. y. x. P(x,y,z). x. r. y. P’(x,y,0).

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Spherical coordinates

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  1. Spherical coordinates z y x

  2. Spherical coordinates z y x P(x,y,z)

  3. Spherical coordinates z y x P(x,y,z) P’(x,y,0)

  4. Spherical coordinates z y x P(x,y,z) x y P’(x,y,0)

  5. Spherical coordinates z y x P(x,y,z) x r y P’(x,y,0)

  6. Spherical coordinates z y x P(x,y,z) x r y P’(x,y,0)

  7. Spherical coordinates z y x P(x,y,z) x r y P’(x,y,0)

  8. Spherical coordinates z y x Q P(x,y,z) x r y P’(x,y,0)

  9. Spherical coordinates z y x Q P(x,y,z) ? ? x r y P’(x,y,0)

  10. Spherical coordinates z y x Let’s label the origin O,and consider the triangles OPQ and OPP’ Q P(x,y,z) ? O x r y P’(x,y,0)

  11. Spherical coordinates z y x Right triangle trig gives us everything we need to know! Q P(x,y,z) ? O x r y P’(x,y,0)

  12. Spherical coordinates z y x Q P(x,y,z) ? ? z O x r y P’(x,y,0)

  13. Let’s pull out that triangle for a closer look z

  14. Let’s pull out that triangle for a closer look z

  15. Spherical coordinates z y x Q P(x,y,z) ? ? O x r y P’(x,y,0)

  16. Spherical coordinates z y x Q P(x,y,z) ? ? O x r y P’(x,y,0)

  17. So we know: And since

  18. Spherical Coordinates

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