Convert to Rectangular Coordinates 9 2 r 1 sin thetaSoluti

Convert to Rectangular Coordinates (9, 2) r = 1 + sin theta

given

(a) ( 9,2 )

we know point in rectangular is ( x-coordinate , y-coordinate )

therefore from given point x = 9 and y = 2

( b )

r = 1 + sin(theta )

multiply r on both sides

then r^2 = r + rsin(theta)

we know x =rcos(theta) , y= rsin(theta) and tan(theta) = y/x

from above r^2 = x^2 + y^2 = r^2

and r = sqrt( x^2 + y^2 )

there fore x^2 + y^2 = sqrt( x^2 + y^2 ) + y

or y = x^2 + y^2 - sqrt( x^2 + y^2 )