Converting Cartesian to Polar: Finding the Polar Equation

[ThiagoG]

Homework Statement

Find a polar equation for the curve represented by the Cartesian equation.

y=1+3x

Homework Equations

x²+y²=r²
x=Rcos(θ)
y=Rsin(θ)

The Attempt at a Solution

(1+3x)²+x²=r²
1+6x+10x²=r²
1+6rcos(θ)+10r²cos²(Θ)=r²

 

[HallsofIvy]

Why are you squaring? This will give you a relation between $x^2$ and $y^2$, not x and y, and so not the original equation. Just replace "x" with $r cos(\theta)$ and "y" with $r sin(\theta)$ in the original equations.

 

[ThiagoG]

Why are you squaring? This will give you a relation between $x^2$ and $y^2$, not x and y, and so not the original equation. Just replace "x" with $r cos(\theta)$ and "y" with $r sin(\theta)$ in the original equations.

Oh thank makes a lot of sense. Thank you.