130 



Dr. L. Silber stein : Further Contributions 



points of the unit vectors i, a, "b, and if the unit vector j be 

 normal to i, we have, by what has been explained previously, 



a = icos a +j sin a, 



"b = icos/3 — j sin/3, 



whence, by the distributive law of multiplication, 



ab= cos (« + /3)= cos a . cos/3— sin a . sin ft, (12c) 



whence also, by (126), after easy transformations, 



sin (a + j3) = sin a . cos /3 + cos a . sin /3, . (12c) 



as in ordinary trigonometry. 



Fig. 6. 



/ 



Leaving other details to the reader, let us still notice that 

 tan 6= tan (a, 1>) can be denned either by 



tan 6 = sin 0/cos 0, 

 or graphically (fig. 6) by 



tan d=± \a SI, 



(12*) 



