36 



MATHEMATICAL FORMULA AND ELLIPTIC FUNCTIONS 



2.114 If p, the perpendicular to the line from the origin, makes an angle /3 

 with the axis: 



p = r cos (6 - 0). 



2.130 Area of polygon whose vertices are at x i} y\; x*, y^\ ........ 



#n, y n = A. 



2A = yi(x n - xz) + y z (xi - X*) + yz(x 2 - z 4 ) + ...... + y n (x n -i - *i). 



PLANE CURVES 



2.200 The equation of a plane curve in rectangular coordinates may be given 

 in the forms: 



(a) ?=/(*) 



(b) x =/i(/), y =/2(0- The parametric form, 



(c) Ffey) = o. 



2.201 If r is the angle between the tangent to the curve and the #-axis: 



(a) tan T = / = y' . 

 dx 



(b) tan T = 



df*(t) 

 dt 



dt 



(c) tan T = - 



dx 



In the following formulas, 

 y' = & = tan r (2.201). 

 2.202 OM = x, MP = y, angle ^TP = r. 



FIG. 2 



TP = y esc T 



= tangent, 



TM = y cot r = ^7 = subtangent, 



PN = y sec r = y Vi + ^ /2 = normal, 



MN = y tan T = yy' = subnormal. 



2.203 Or = x -- 7 = intercept of tangent on #-axis, 



OT' = y - xy' = intercept of tangent on y-axis, 

 ON = x + yy' = intercept of normal on #-axis, 



ON' = y + = intercept of normal on y-axis. 



