USEFUL FORMULAS. 



XV 



g. Relations of natural logarithms to other logarithms. 

 B =■ base of any system, 

 JV= any number, 

 Z = log iVto base /> = log^TV^ 

 / = log N to base e = los^JV. 



Then 



'toe-' 



L = I \ogne = ^/log,.B, 



logr,e^ i/\og,B = IX, saj^, which is called the modulus of the system whose base 

 is B. In the common, or Briggean system, 



it- = login^ = 0.43429448 .... 

 log /x = 9.6377843 - 10. 



2. Trigonometric Formulas. 

 a. Signs of trigonometric functions. 



b. Values of functions for special angles. 



c. Fundamental formulas. 



Sin^ a -|- cos'' a =: I, 



cos a sec a = I, 



sin a 



tan a = , 



cos a 



1 -\- tzn^ a = s— = sec- a, 



' COS- a ' 



sm a 



I + cot^ a = . o = cosec^ a, 



versed sin a = i — cos a. 



