Examples of Groups 3 



To visualize our results, take an angle a, not an integral mul- 

 tiple of 77- /S, and place in the standard position, vertex at origen 

 ami positive .r-axis for initial line. If the other angles be like- 

 wise thought of as in standard position, their terminal lines will 

 lie as in the diagram below. 



oc-y=o 



y* 



*y-£ 



Geometrically then — 



Multiplication by unity leaves the terminal line alone. 

 Multiplication by .s reflects it upon the y-axis. 

 Multiplication by c reflects it upon the line x — ;y=o. 

 Multiplication by sc turns it forward tt/2. 

 Multiplication by cs turns it backward tt/2. 

 Multiplication by ses reflects it upon the line x-\-y=o. 

 Multiplication by <~sr reflects it upon the .r-axis. 

 Multiplication by (sc} 2 turns it forward or backward it. 



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