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The result of converting 150 degrees to radians is approximately 2.6180 radians.
To convert degrees to radians, we multiply the degree value by π and divide by 180. Since 150 degrees is a measure of an angle, we need to express it in radians which are based on the radius of a circle. The formula ensures that the angle’s measure is consistent with the circle’s arc length, making it useful in mathematical calculations involving angles and circles.
Conversion Result and Explanation
150 degrees equals about 2.6180 radians. This is because 1 degree is equal to π/180 radians, so multiplying 150 by π/180 yields the radian measure.
Conversion Tool
Result in radian:
Conversion Formula
The conversion from degrees to radians is based on the fact that a full circle equals 2π radians and 360 degrees. The formula is radians = degrees × π / 180. This works because it scales the degree measure into the radian measure, which is proportional to the circle’s arc length. For example, to convert 150 degrees, multiply 150 by π/180, which simplifies to 5π/6, approximately 2.6180 radians.
Conversion Example
- Convert 45 degrees to radians:
- Multiply 45 by π/180.
- 45 × π/180 = π/4.
- π/4 ≈ 0.7854 radians.
- Convert 90 degrees to radians:
- Multiply 90 by π/180.
- 90 × π/180 = π/2.
- π/2 ≈ 1.5708 radians.
- Convert 120 degrees to radians:
- Multiply 120 by π/180.
- 120 × π/180 = 2π/3.
- 2π/3 ≈ 2.0944 radians.
- Convert 180 degrees to radians:
- Multiply 180 by π/180.
- 180 × π/180 = π.
- π ≈ 3.1416 radians.
Conversion Chart
| Degree | Radian |
|---|---|
| 125.0 | 2.1817 |
| 130.0 | 2.2689 |
| 135.0 | 2.3562 |
| 140.0 | 2.4435 |
| 145.0 | 2.5307 |
| 150.0 | 2.6180 |
| 155.0 | 2.7053 |
| 160.0 | 2.7925 |
| 165.0 | 2.8798 |
| 170.0 | 2.9671 |
| 175.0 | 3.0543 |
This chart shows degrees from 125 to 175 and their equivalent in radians. Use this to quickly find the radian value for specific degree measures.
Related Conversion Questions
- How many radians is 150 degrees?
- What is the radian equivalent for 150°?
- Convert 150 degrees into radians manually?
- Why is 150 degrees equal to approximately 2.618 radians?
- What is the formula to change degrees to radians for 150°?
- How do I convert an angle of 150 degrees to radians using a calculator?
- Is 150 degrees more or less than π radians?
Conversion Definitions
Degree
A degree is a unit of angle measurement where a full circle is divided into 360 equal parts, making each part one degree. It’s used in geometry, navigation, and various sciences to quantify the size of angles or rotations.
Radian
A radian is a measure of an angle based on the radius of a circle, where an angle’s measure is the ratio of the arc length to the radius, with one radian being the angle subtended by an arc equal in length to the radius of the circle. It’s a natural way to measure angles in mathematics.
Conversion FAQs
Why does multiplying degrees by π/180 convert to radians?
This works because π radians equal 180 degrees, so multiplying degrees by π/180 scales the degree measure into the radian system, maintaining the proportional relationship between the circle’s arc length and its radius.
Can I convert degrees to radians without a calculator?
Yes, by using the formula degrees × π/180 or by remembering common conversions like 90°, 180°, etc., then applying the formula manually or estimating using known values of π.
What is the radian measure of 150 degrees?
150 degrees equals 5π/6 radians, which is approximately 2.6180 radians, obtained by multiplying 150 by π/180.
How does the conversion change if I use a different value of π?
The conversion relies on π being approximately 3.1416; using a different approximation affects the result slightly, but using the standard π ensures accurate calculations.
