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58 degrees equals approximately 1.011 radian.
To convert degrees to radian, multiply the degree value by π divided by 180. This works because 180 degrees is equal to π radians, so the conversion factor is π/180. For 58 degrees, multiplying 58 by π/180 gives the radian measure.
Conversion Result and Explanation
Conversion Tool
Result in radian:
Conversion Formula
The formula to convert degrees to radian is: radians = degrees × (π / 180). This formula works because a full circle contains 360 degrees, which is equal to 2π radians. Dividing π by 180 converts the degree measure into radian measure, ensuring the units align.
For example, to convert 58 degrees:
- Multiply 58 by π, which is approximately 3.1416.
- Calculate 58 × 3.1416 = 181.4816.
- Divide 181.4816 by 180 to get 1.0082 radians.
Conversion Example
Convert 45 degrees to radian:
- Multiply 45 by π (3.1416): 45 × 3.1416 = 141.372.
- Divide 141.372 by 180: 141.372 / 180 = 0.7854 radian.
Convert 90 degrees to radian:
- Multiply 90 by π: 90 × 3.1416 = 282.744.
- Divide 282.744 by 180: 282.744 / 180 = 1.5708 radian.
Convert 30 degrees to radian:
- Multiply 30 by π: 30 × 3.1416 = 94.248.
- Divide 94.248 by 180: 94.248 / 180 = 0.5236 radian.
Conversion Chart
| Degrees | Radian |
|---|---|
| 33.0 | 0.5767 |
| 34.0 | 0.5934 |
| 35.0 | 0.6109 |
| 36.0 | 0.6283 |
| 37.0 | 0.6458 |
| 38.0 | 0.6632 |
| 39.0 | 0.6807 |
| 40.0 | 0.6981 |
| 41.0 | 0.7156 |
| 42.0 | 0.7330 |
| 43.0 | 0.7505 |
| 44.0 | 0.7680 |
| 45.0 | 0.7854 |
| 46.0 | 0.8029 |
| 47.0 | 0.8203 |
| 48.0 | 0.8378 |
| 49.0 | 0.8552 |
| 50.0 | 0.8727 |
| 51.0 | 0.8901 |
| 52.0 | 0.9076 |
| 53.0 | 0.9250 |
| 54.0 | 0.9425 |
| 55.0 | 0.9599 |
| 56.0 | 0.9774 |
| 57.0 | 0.9948 |
| 58.0 | 1.0123 |
| 59.0 | 1.0298 |
| 60.0 | 1.0472 |
| 61.0 | 1.0647 |
| 62.0 | 1.0821 |
| 63.0 | 1.0995 |
| 64.0 | 1.1170 |
| 65.0 | 1.1345 |
| 66.0 | 1.1519 |
| 67.0 | 1.1694 |
| 68.0 | 1.1868 |
| 69.0 | 1.2043 |
| 70.0 | 1.2217 |
| 71.0 | 1.2392 |
| 72.0 | 1.2566 |
| 73.0 | 1.2741 |
| 74.0 | 1.2915 |
| 75.0 | 1.3090 |
| 76.0 | 1.3265 |
| 77.0 | 1.3439 |
| 78.0 | 1.3614 |
| 79.0 | 1.3788 |
| 80.0 | 1.3963 |
| 81.0 | 1.4138 |
| 82.0 | 1.4312 |
| 83.0 | 1.4487 |
Use this chart to quickly find the radian equivalent for degrees in this range, by matching the degree value in the first column to your needs.
Related Conversion Questions
- How many radians are in 58 degrees?
- What is 58 degrees expressed in radians?
- Convert 58 degrees to radians manually?
- What is the radian measure of 58 degrees?
- How do I change 58 degrees to a radian value?
- Is 58 degrees equal to 1.01 radians?
- What is the conversion factor from degrees to radian for 58 degrees?
Conversion Definitions
Degrees are units of angular measurement where a full circle is divided into 360 equal parts, making each degree a 1/360th part of a circle. Radians are units of angular measure based on the radius of a circle, where an angle in radians is the length of the arc it subtends divided by the radius.
Conversion FAQs
Why do we convert degrees to radians in mathematics?
Converting degrees to radians is necessary because many mathematical functions, especially in calculus, are defined in terms of radians. Radians provide a natural measure for angles that simplifies formulas involving trigonometric functions and derivatives.
Can I convert degrees to radians without a calculator?
Yes, by using the formula radians = degrees × (π / 180). For example, for 58 degrees, multiply 58 by π/180, which can be approximated as 3.1416/180, and then multiply the two numbers. This gives a close estimate without a calculator.
What is the significance of π in the degree to radian conversion?
π relates to radians because a full circle equals 2π radians, which corresponds to 360 degrees. The presence of π in the formula reflects the inherent relationship between the two units, linking angular measures to the circle’s geometry.
How precise is the conversion from degrees to radian?
The conversion’s accuracy depends on the precision of π used. Using an approximation like 3.1416 gives a result close to the exact value, but for high-precision needs, more decimal places of π should be used.
Is there a quick way to remember the degrees-to-radian formula?
Yes, remember that radians = degrees × (π / 180). Think of it as converting degrees into a fraction of π, where 180 degrees equals π radians, and use that proportional relationship for any degree value.
