76 



PRACTICAL MATHEMATICS 



Also 



AQ 



and AQ = r sin sin <f> 



If x, y, z are the rectangular co-ordinates of the point P, they 

 can be expressed in terms of the polar co-ordinates. 

 x = AO = r cos sin < 

 y = AQ = r sin sin < 

 z = OC = r cos < 



h-^ 



i *V-^ 



Q 



FIG. 24. 



Conversely, the polar co-ordinates can be expressed in terms of 

 the rectangular co-ordinates. 



r = V^ 2 + y z + z z 



tan = y - 



x 



C S = ./ o . O . 9 



If a, (3, and y are the angles OP makes with the axes OX, OY, 

 and OZ respectively, and I, m, and n are the corresponding 

 direction cosines 



x 

 I = cos a = - 



= cos sin < 

 m = cos p = ^ 



= sin sin < 



2 



n = cos y = - 

 r 



= cos <> 



