Which of the following is a polar equation for the curve represented by the Cartesian equation $x^2+y^2=3$?

• A. $r=\sqrt{2}$
• B. $r=\sqrt{3}$
• C. $r=1$
• D. $r=3$

Answer: (B)

Verified step by step guidance

1. Recall that the Cartesian equation given is \(x^2 + y^2 = 3\), which represents a circle centered at the origin with radius \(\sqrt{3}\).
2. Remember the relationship between Cartesian and polar coordinates: \(x = r \cos{\theta}\) and \(y = r \sin{\theta}\).
3. Substitute \(x\) and \(y\) in the Cartesian equation with their polar forms: \((r \cos{\theta})^2 + (r \sin{\theta})^2 = 3\).
4. Simplify the equation using the Pythagorean identity \(\cos^2{\theta} + \sin^2{\theta} = 1\), which gives \(r^2 = 3\).
5. Take the square root of both sides to express \(r\) in terms of a constant: \(r = \sqrt{3}\), which is the polar equation of the circle.