Convert the rectangular equation 2y - 3x = 2 to polar form?

Answer 1

x = r cos (theta) and y = r sin(theta)

Let T=theta

2rsinT - 3r cosT = 2
factor out r
r(2sinT - 3cosT) = 2
divide by coefficeint to isolate r
r = 2 / (2sinT - 3 cosT)

:)

Answer 2

Where are you getting stuck? You have equations in your book to convert between polar and rectangular coordinates, right? Substitute the proper values for x and y (r cos theta & r sin theta), and then solve for r in terms of theta.

Answer 3

Remember the identities:

x = rcosθ
y = rsinθ

Convert to polar.

2y - 3x = 2

2rsinθ - 3rcosθ = 2

r(2sinθ - 3cosθ) = 2

r = 2 / (2sinθ - 3cosθ)

Answer 4

Remember that x = r*cos(Q) and y = r*sin(Q)
(Q is the symbol I'm using for theta)

So just plug those into the equation that you have.
2r*sin(Q) - 3r*cos(Q) = 2
And simply solve for 'r'
r(2sin(Q) - 3cos(Q)) = 2
r = 2 / (2sin(Q) - 3cos(Q))

And there's the equation you're looking for.