Question

Yes or No? If No, give a reason.

Do the equations relating polar and rectangular coordinates uniquely determine r and $\theta$

Short answer

No

Step-by-step solution

Step 1. Given information

Rectangular and polar coordinate system

Step 2. Concept used

Uniquely determine means for a point in rectangular coordinates, there is a unique point in a polar coordinate system with respect to that point. But there can be more than one point in polar coordinates for a particular point in a rectangular system.

Step 3. Calculation

As we use these formulae for converting in polar coordinate,

$r=\pm \sqrt{x^2+y^2}\&\tan \left(\theta \right)=\frac{y}{x}$

Through these formulae, we can see that there is more than one value of radius for a particular point in the rectangular coordinate system.