42 MATHEMATICAL FORMULA AND ELLIPTIC FUNCTIONS 



2.273 - dr 



sin 6 -TQ + r cos u 



du 



tan r = - - - 

 n dr . a 



cos -72 ^ sin u 

 du 



= r\J I + ( V= polar tangent 



PF= r 2 + = polar normal 



2.274 



7/3 



OjR = r 2 = polar subtangent 



OF = -72 . = polar subnormal. 



r 2 

 2.275 OQ = . = p = distance of tangent from origin. 



OS = , - = distance of normal from origin. 



2.276 If u = -, the curve r = f(B) is concave or convex to the origin according as 



d 2 u 

 + d6* 



is positive or negative. At a point of inflexion this quantity vanishes and changes 

 sign. 



2.280 The radius of curvature is, 



~ r 



2.281 If u = - the radius of curvature is 

 r 



7 , d*u 

 ( U + W 



