POLAR CO-ORDINATES 



Length = 2 1 \/r 2 



= 2V2af(l - cos 8)- 

 Jo 



283 



f* 6 



4al sin- 



Jo ^ 



rf0 



*= 8a cos - cos I 



8a 



150. Example 2. Transform the equation x 3 + f/ 3 = &n/ into 

 polar co-ordinates, and then find the area of the loop. 



Then 



r 3 cos 3 + r 3 sin 3 = 3r 2 sin cos 

 3 sin cos 



sin 3 + cos 3 



Now r = when has the values and -, and so the loop 



JB 



evidently occurs between these values of 0. 



To draw the loop, give some intermediate values and calculate 

 the corresponding values of r. 



FIG. 93- 



