How do i convert the polar equation r^2=Sin(theta)*Cos(theta) into a rectangular equation?

Question

I think i have to divide both sides by r^2, but i'm not sure what to do after that.

Answer 1

In converting from polar to rectangular coordinates remember that r^2 = x^2 + y^2, theta = arctan(y/x);

The r^2 part of your eq. is easy. As for the theta, tan(theta)=y/x Draw a right triange with sides y (vertical) and x (horizontal). The ange opposite y is theta. The hypotenuse of this triangle is sqrt(x^2+y^2). Therefore the sin(theta) is side opposite (y) divided by the hypotenuse [sqrt(x^2+y^2)]. Also cos(theta) is side adjacent (x) divided by the hypotenuse. You now have all the information to subsitute for r^2, sin(theta) and cos(theta) in your equation.

Answer 2

Remember: y = r*sen(theta) and x = r*cos(theta) in the change of coordinates. I'll write t for theta (shorter). So; r = 2*sin(t) *** multiply both sides by r r^2=2*r*sin(t) *** remember 1 = cos^2(t)+sin^2(t) r^2*(cos^2(t)+sin^2(t))=2*r*sin(t) *** change coordinates x^2+y^2=2y *** add 1 to both sides x^2+y^2-2y+1=1 X^2+(y-1)^2=1 *** done Cheers