Convert to polar form. Solve for r. 3x+y=4

Answer 1

When converting between Cartesian and polar coordinates, there are three key equations you should always keep in mind:

1) x = r*cosθ

2) y = r*sinθ

3) x^2 + y^2 = r^2

If you can remember those three, then almost every single conversion becomes a matter of substitution and using algebra to solve for a variable.

In this case, we have the equation 3x + y = 4. So, if we substitute our polar values for x and y we get:

3(r*cosθ) + (r*sinθ) = 4

3r*cosθ + r*sinθ = 4

and from there it's just isolating the variable!

r(3cosθ + sinθ) = 4

⇒ r = 4 / (3cosθ + sinθ)

I hope this helps, and please let me know if you need more clarification.

Answer 2

James

Use x = r*cos(θ) and y = r*sin(θ)

3x+y=4 means 3*r*cos(θ) + r*sin(θ) =4

factor out the r and simplify.