Converting to Rectangular Form

[Relz]

I need to convert r= 4 + 4 cos (theta) into rectangular form but i'm not sure how to do it since it's not in polar form. Or is it and I can't tell? I just need someone to guide me in the right direction!

Thanks in advance!

 

[daon2]

Recall that \(\displaystyle r=\sqrt{x^2+y^2}\) and \(\displaystyle r\cos\theta = x\)

 

[Relz]

Recall that \(\displaystyle r=\sqrt{x^2+y^2}\) and \(\displaystyle r\cos\theta = x\)

Okay so I converted and solved until I got: 0= x² + y² - 4x -16
I did a square root and now I have 0= -x + y - 4

I have no idea how to turn this into rectangular form. Any ideas?

 

[daon2]

Okay so I converted and solved until I got: 0= x² + y² - 4x -16
I did a square root and now I have 0= -x + y - 4

I have no idea how to turn this into rectangular form. Any ideas?

That is not correct. What you have above is the equation of a circle. Your original function of r and theta is a Cardioid (Wikipedia)

I'm also uncertain as how you got to the second equation from the first. You are aware that \(\displaystyle \sqrt{a+b}\neq \sqrt{a}+\sqrt{b}\) right?

Please post your substitutions and your step-by-step simplification.

 

[Relz]

That is not correct. What you have above is the equation of a circle. Your original function of r and theta is a Cardioid (Wikipedia)

I'm also uncertain as how you got to the second equation from the first. You are aware that \(\displaystyle \sqrt{a+b}\neq \sqrt{a}+\sqrt{b}\) right?

Please post your substitutions and your step-by-step simplification.

I multiplied both sides by r. Then converted r² to x² + y² so that I had: x² + y² = 4 (sqrt{x² + y² }) + 4x

 

[daon2]

I multiplied both sides by r. Then converted r² to x² + y² so that I had: x² + y² = 4 (sqrt{x² + y² }) + 4x

Okay, great. That is in rectangular coordinates now. That should be the answer, unless it is required for you to put it into some kind of standard form. Note, you won't be able to "solve for y" here in one explicit equation.