Math Problem Statement

Convert the radian measure to degrees.

22

...

Question content area right

Part 1

22

​radian(s)equals=enter your response heredegrees°enter your response here​'

​(Round to the nearest ​minute.)

Solution

To convert radians to degrees, we use the following formula:

Degrees=Radians×(180π)\text{Degrees} = \text{Radians} \times \left( \frac{180^\circ}{\pi} \right)

Given that the radian measure is 22 radians, the conversion becomes:

Degrees=22×(180π)\text{Degrees} = 22 \times \left( \frac{180^\circ}{\pi} \right)

Let's calculate that.

Degrees=22×(1803.14159)22×57.2958=1260.51\text{Degrees} = 22 \times \left( \frac{180^\circ}{3.14159} \right) \approx 22 \times 57.2958 = 1260.51^\circ

To round to the nearest minute, we take the decimal part (.51), which represents the fraction of a degree. To convert that into minutes (since there are 60 minutes in a degree), we multiply:

0.51×60=30.6 minutes0.51 \times 60 = 30.6 \text{ minutes}

So, rounding to the nearest minute, the result is approximately:

1260311260^\circ 31'

Final Answer:
22 radians ≈ 1260° 31'

Would you like more details on the steps, or have any questions about this? Here are some related questions to explore further:

  1. How do you convert from degrees back to radians?
  2. What is the relationship between radians and arc length in a circle?
  3. What are some practical applications of radians in real life?
  4. How do you convert other angle units, like gradians or mils, to degrees?
  5. What are the common errors in converting between radians and degrees?

Tip:
When converting between radians and degrees, always make sure you use the value of π as approximately 3.14159 for higher accuracy.

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Angle Conversion

Formulas

Degrees = Radians × (180°/π)

Theorems

Radian-degree conversion theorem

Suitable Grade Level

Grades 9-12