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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!

Convert the following degree measure to radian measure: 58° 20'.

Learn how to convert the angle 58° 20' from degrees to radians using a step-by-step method. This trigonometry problem involves key concepts of angle conversion and is suitable for students in Grades 9-12.

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