POLAR CO-ORDINATES 



279 



- COS J - COS - 



3<-i-i>-<->-i>] 



(/) To find the height of the centroid of the cycloidal curve 

 ibove the base. 



By symmetry, the centroid is evidently situated in the vertical 

 centre line. Let y c be the height. 



Then 



ox 



147. Polar Co-ordinates. If P is a point whose rectangular 

 co-ordinates are x, y, its position with respect to the axes 

 of reference can also be determined by means of a distance r 

 measured from the origin along a radial line which is inclined to 

 the axis OX at an angle 6. r and are spoken of as the polar 

 co-ordinates of the point. (Fig. 90.) 







FIG. 90. 



The relations between the rectangular and polar co-ordinates 

 in be very easily determined. 



