To solve part (b) and convert the rectangular coordinates $(-10, 34)$ into polar coordinates, we use the following formulas:

1. Polar Radius (r): $r = \sqrt{x^2 + y^2}$ where $x = -10$ and $y = 34$.

2. Polar Angle ($\theta$): $\theta = \tan^{-1}\left(\frac{y}{x}\right)$ Here, the angle must be adjusted based on the quadrant. Since $x < 0$ and $y > 0$, the point is in the second quadrant, so we add $180^\circ$ to the angle.

Let's compute these values.

1. Calculate $r$: $r = \sqrt{(-10)^2 + (34)^2} = \sqrt{100 + 1156} = \sqrt{1256} \approx 35.45$

2. Calculate $\theta$: $\theta = \tan^{-1}\left(\frac{34}{-10}\right) = \tan^{-1}(-3.4)$ The arctangent of $-3.4$ gives an angle of approximately $-73.74^\circ$. Since we are in the second quadrant, we add $180^\circ$: $\theta = 180^\circ - 73.74^\circ = 106.26^\circ$

Final Answer (Polar Coordinates): $(35.45, 106.26^\circ)$

Let me know if you want further clarification or detailed steps!

Here are some related questions to expand your understanding:

1. How can you confirm the quadrant of a point from rectangular coordinates?
2. What are the key differences between polar and rectangular coordinates?
3. How do you calculate polar coordinates when the point lies on an axis?
4. What happens to the polar angle $\theta$ when both $x$ and $y$ are negative?
5. How do you convert polar coordinates back into rectangular coordinates?

Tip: Always adjust the angle $\theta$ based on the quadrant to ensure accurate polar coordinate conversion!