To convert the rectangular coordinates $(-10, 0)$ into polar coordinates, we use the formulas:

1. Radius (r): $r = \sqrt{x^2 + y^2}$ Here, $x = -10$ and $y = 0$: $r = \sqrt{(-10)^2 + 0^2} = \sqrt{100} = 10$

2. Angle ($\theta$): $\theta = \arctan\left(\frac{y}{x}\right)$ For $x = -10$ and $y = 0$, the angle is directly on the negative x-axis, so: $\theta = \pi \, \text{(since it is 180 degrees in radians)}.$

The polar coordinates are therefore: $(10, \pi)$

Final Answer:

$(10, \pi)$

Would you like further details on the process or have any other questions?

5 Related Questions:

1. How do you convert polar coordinates back to rectangular coordinates?
2. What is the general formula for converting coordinates in the second quadrant?
3. Why is the radius always positive in standard polar coordinates?
4. How do angles in radians relate to degrees?
5. What happens if the radius $r$ is negative in polar coordinates?

Tip: Always ensure angles are expressed in the correct range for polar coordinates (typically $0 \leq \theta < 2\pi$).