MATHEMATICS 



19 



Besides these functions, use is sometimes made in railroad 

 work of the versed sine, which is 1 minus the cosine of the 



b 

 angle, or 1 , and the cover 'sed sine, which is 1 minus the 



sine of the angle, or 1 . 

 c 



A good conception of the trigonometric functions may be 

 formed from the diagram, shown in Pig. 2, in which the radius 



Cotangent 



FIG. 2 



ot the circle is assumed as unity. Each ratio denning a trigono- 

 metric function is represented by a single line, as the denomi- 

 nate! is in each case the radius, or unity. 



The six angular functions are so related to each other as to 

 enable the calculations of all when any one of them is known. 

 These relations are given in the table on page 23. 



For angles greater than 90, the functions are expressed by 

 those of acute angles. The rules and formulas relating thereto 

 are given in the table on page 21. As an example, the cosine of 

 210 is found by lormula 33; thus, cos (180+30) = -cos 30. 



