To convert the given rectangular coordinates $(5, 5)$ to polar coordinates, we use the following formulas:

1. Radius (r): $r = \sqrt{x^2 + y^2}$ where $x = 5$ and $y = 5$.

2. Angle (θ): $\theta = \tan^{-1}\left(\frac{y}{x}\right)$ where $x = 5$ and $y = 5$, and we want the angle in degrees.

Step 1: Calculate the radius $r$

$r = \sqrt{5^2 + 5^2} = \sqrt{25 + 25} = \sqrt{50} \approx 7.071$

Step 2: Calculate the angle $θ$

$\theta = \tan^{-1}\left(\frac{5}{5}\right) = \tan^{-1}(1)$ From a standard trigonometric table, we know: $\theta = 45^\circ$

Final Polar Coordinates:

The polar coordinates are $(r, \theta) = (7.071, 45^\circ)$.

Would you like further details on the steps or have any questions? Here are 5 related questions to explore further:

1. How would the polar coordinates change if the point was $(-5, 5)$?
2. How do we convert polar coordinates back to rectangular coordinates?
3. What would the polar coordinates be if the rectangular point was on the y-axis, like $(0, 5)$?
4. How does the tangent inverse function help in finding the angle in polar coordinates?
5. What is the significance of the radius $r$ in polar coordinates?

Tip: Always pay attention to the quadrant of the point to ensure the correct angle is used for the polar coordinates.