To convert the Cartesian coordinates $(5, 5)$ to polar coordinates, we follow these steps:

1. Calculate the radius $r$: $r = \sqrt{x^2 + y^2}$ Substituting the given coordinates $(5, 5)$: $r = \sqrt{5^2 + 5^2} = \sqrt{25 + 25} = \sqrt{50} = 5\sqrt{2} \approx 7.07$

2. Calculate the angle $\theta$ in radians: $\theta = \tan^{-1}\left(\frac{y}{x}\right)$ Substituting the given coordinates $(5, 5)$: $\theta = \tan^{-1}\left(\frac{5}{5}\right) = \tan^{-1}(1) = \frac{\pi}{4} \approx 0.79 \text{ radians}$

Therefore, the polar coordinates of the point $(5, 5)$ are approximately: $(r, \theta) = (7.07, 0.79)$

Would you like more details or have any questions? Here are some related questions:

1. What are the formulas for converting Cartesian coordinates to polar coordinates?
2. How do you find the radius $r$ in polar coordinates?
3. How do you find the angle $\theta$ in polar coordinates?
4. Why is the angle $\theta$ expressed in radians?
5. Can you convert polar coordinates back to Cartesian coordinates?
6. What is the significance of the tangent function in finding $\theta$?
7. How do you handle coordinates in different quadrants when converting to polar form?
8. What are some practical applications of polar coordinates?

Tip: When converting to polar coordinates, always consider the quadrant of the original Cartesian coordinates to determine the correct angle $\theta$.