barrons question on polar curve

TeamRocketGrunt
Fri, 06 Dec 2013 16:15:33 +0000

1/(sin+cos)=r
rsin+rcos=1
rsin=x
rcos=y

So, rsin+rcos=1=x+y
x+y=1 which is the same as 1-x=y
If x=0, y=1 (y intercept); if y=0, x=1 (x intercept). The sides are the distance from the origin to the x-intercept and the distance from the origin to the y-intercept; therefore, this line forms a right triangle with the x and y axes that has leg lengths of 1. The area of a triangle is (1/2)(bh). b and h, in this case, both equal 1, so area=1/2.