The result of converting 150 degree to radian is approximately 2.6179 radians.
To convert 150 degrees into radians, we multiply the degree value by π divided by 180. This works because there are π radians in 180 degrees, so the conversion factor is π/180. For example, 150 × (π/180) equals 150π/180, which simplifies to 5π/6, approximately 2.6179 radians.
Conversion of 150 Degree to Radian
Result in radian:
Conversion Formula
The formula to convert degree to radian is: Radian = Degree × π / 180. This formula works because a full circle contains 2π radians, which equals 360 degrees, so dividing by 180 scales degrees into radians. For example, 150 degrees is calculated as 150 × π / 180 = 5π/6 radians.
Conversion Example
- Convert 90 degrees to radian:
- Step 1: Multiply 90 by π.
- Step 2: Divide the result by 180.
- Calculation: (90 × π) / 180 = π/2 ≈ 1.5708 radians.
- Convert 45 degrees to radian:
- Step 1: 45 × π = 45π.
- Step 2: Divide by 180.
- Calculation: 45π / 180 = π/4 ≈ 0.7854 radians.
- Convert 180 degrees to radian:
- Step 1: 180 × π = 180π.
- Step 2: Divide by 180.
- Calculation: 180π / 180 = π ≈ 3.1416 radians.
Conversion Chart
| Degrees | Radians |
|---|---|
| 125.0 | 2.1817 |
| 130.0 | 2.2689 |
| 135.0 | 2.3562 |
| 140.0 | 2.4435 |
| 145.0 | 2.5307 |
| 150.0 | 2.6179 |
| 155.0 | 2.7053 |
| 160.0 | 2.7925 |
| 165.0 | 2.8798 |
| 170.0 | 2.9671 |
| 175.0 | 3.0543 |
This chart helps you quickly find radian equivalents for degrees between 125 and 175. Read the degree value on the left and see the corresponding radian on the right.
Related Conversion Questions
- What is the radian equivalent of 150 degrees?
- How do I convert 150 degrees into radians manually?
- What is 150 degrees in terms of π radians?
- Can you show me the formula to change 150 degrees to radians?
- What is the radian measure for 150 degrees?
- How many radians are in 150 degrees?
- What is the result of converting 150 degrees to radian with calculator?
Conversion Definitions
A degree is a unit of angle measurement, with 360 degrees making a full circle, used mainly in geometry and navigation. A radian measures angles based on the radius of a circle, where one radian equals the angle subtended by an arc equal in length to the radius.
Conversion FAQs
How accurate is the approximation of 150 degrees in radians?
The conversion of 150 degrees to radians results in approximately 2.6179, which is accurate to four decimal places. Since π is an irrational number, the exact value is 5π/6 radians, but the decimal approximation is sufficient for most practical purposes.
Why is the conversion factor π/180 used in the formula?
The factor π/180 comes from the fact that 180 degrees equals π radians. Using this ratio ensures that degree measurements are correctly scaled into radian measurements based on the circle’s geometry.
Can I convert degrees to radians with a calculator?
Yes, most scientific calculators have a conversion function or can be used to perform the multiplication directly. Just multiply the degree value by π and divide by 180 for an accurate result.
Is there a difference between degree and radian in measuring angles?
Yes, degrees divide a circle into 360 parts, while radians measure based on the circle’s radius, with one radian being the angle where the arc length equals the radius. Radians often simplify mathematical formulas involving circles and trigonometry.
What is the significance of converting degrees to radians?
Converting degrees to radians is important because many mathematical functions, especially in calculus and trigonometry, require angles in radians for correct calculations and formulas to work properly.