CHAPTER XX. 



TANGENTS AND ASYMPTOTES OF CURVES REFERRED TO 

 POLAR CO-ORDINATES. 



278. IF we have the equation to a curve expressed in 

 terms of x and y, we may transform it to one between polar 

 co-ordinates by assuming sc = r cos 6 and y = r sin 6. Thus 

 r becomes a function of 6, and the equation to a curve in polar 

 co-ordinates takes the form r =f(0), or F (r, 6) = 0. In this 

 case the curve is called a polar curve or spiral; r is called the 

 radius vector and 6 the vectorial angle. 



The angle (-^) which the tangent to a curve makes with the 

 axis of x is given by the equation 



&> ( Art - 257 )' 



. 



sin -T^ -f- r cos 6 

 dd 

 - - 



-rs 

 do 



279. Expression for the angle included between the radius 

 vector at-any point of a curve, and the tangent to the curve at 

 that point 



Hence, by Art. 201, 



Let P be a point in a curve, the polar co-ordinates of which 

 are r and 0, S being the pole. 



