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## Homework Statement

(a) Starting from a point on the equator of a sphere of radius

*R*, a particle travels through an angle

*α*eastward and then through an angle

*β*along a great circle toward the north pole. If the initial position is taken to correspond to

*x*=

*R*,

*y*= 0,

*z*= 0, show that its final coordinates are (

*R*cos

*α*cos

*β*,

*R*sin

*α*cos

*β*,

*R*sin

*β*).

(b) Find the coordinates of the final position of the same particle if it first travels through an angle

*α*northward, then changes course by 90° and travels through an angle

*β*along a great circle that starts out eastward.

**2. The attempt at a solution**

This is basically geometry, and I've shown part (a) correctly via a diagram. I don't seem to get the correct answer for part (b) and I suspect I am not interpreting the question correctly.

Attached is a somewhat crude (though the clearest I can produce!) diagram showing how I see the situation for (a) and (b). I haven't added my annotations for my answer for clarity's sake. I get the following for (b):

*x*=

*R*cos

*α*cos

*β*

*y*=

*R*cos

*α*sin

*β*

*z*=

*R*sin

*α*

If someone could tell me whether or not I am interpreting the information correctly (and hence whether it actually

*is*my geometric analysis) I would very much appreciate it. :)