Converting between Cartesian and Polar FunctionsElmer NoconAngelo BernabeMark Kenneth Hitosis

cos

sin

tan

222

rx

ryx

y

ryx1035 xy we substitute r ∙ sin Θ for y103)sin(5 xr

then substitute r ∙ cos Θ for x10)cos(3)sin(5 rr

we factor out r 10)cos3sin5( r

)cos3sin5(

10

)cos3sin5(

)cos3sin5(

r

divide both sides of the equation by (5sin Θ – 3cos Θ)

)cos3sin5(

10

rF I N

A

LANSWE

R

cos

sin

tan

222

rx

ryx

y

ryx96 xy we substitute r ∙ sin Θ for yand r ∙ cos Θ for x respectively9cos6sin rr

subtract (6 r ∙ cos Θ) from both sides of the equation , which will result into this 9cos6sin rrfactor out r9)cos6(sin r

divide (sin Θ - 6cos Θ) from both sides of the equation

)cos6(sin

9

r

F I N A

LANSWE

R

sin7r

cos

sin

tan

222

rx

ryx

y

ryxfrom y = r ∙ sin Θ we convert it to another equation by dividing from both sides of the equation r sin

r

y

r

yr7

then we substitute y/r for sin Θ

cross multiplyyr 72

then we substitute x2 + y2 for r2 yyx 722 F I N

A

LANSWE

R

cossinr

cos

sin

tan

222

rx

ryx

y

ryxfrom y = r ∙ sin Θ we convert it to another equation by dividing from both sides of the equation r sin

r

y

from x = r ∙ cos Θ we convert it to another equation by dividing from both sides of the equation r cos

r

x

then we substitute y/r for sin Θ and x/r for cos Θ respectivelyr

x

r

yr

Then multiply both sides of the equation by rxyr 2 then we substitute x2 + y2 for r2

xyyx 22

F I N A

LANSWE

R

2cr

cos

sin

tan

222

rx

ryx

y

ryx

let’s say that c represents some constant

222 )()( cr then we substitute x2 + y2 for r2 422 cyx

F I N A

LANSWE

R

square both sides of the equation

42 cr