To convert $58^\circ 20'$ (degrees and minutes) to radians, we can follow these steps:

1. Convert the minutes to degrees:
   $20'$ is part of a degree, and there are 60 minutes in a degree. So, we divide 20 by 60 to convert it into degrees: $20' = \frac{20}{60} = 0.3333^\circ$ Thus, $58^\circ 20' = 58^\circ + 0.3333^\circ = 58.3333^\circ$.

2. Convert degrees to radians:
   To convert from degrees to radians, use the formula: $\text{Radians} = \text{Degrees} \times \frac{\pi}{180}$ Substituting $58.3333^\circ$ into the formula: $\text{Radians} = 58.3333 \times \frac{\pi}{180} = 1.0181 \text{ radians}$

So, $58^\circ 20'$ is approximately $1.0181$ radians.

Would you like further clarification or details on any part of this process?

Here are 5 related questions:

1. How do you convert radians back to degrees?
2. What is the significance of radians in trigonometry?
3. How would you convert an angle of $125^\circ 45'$ to radians?
4. What is the relationship between radians and arc length?
5. How do radians simplify certain trigonometric calculations?

Tip: Always remember that $180^\circ$ equals $\pi$ radians, which is the key conversion factor between degrees and radians!