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Degrees and radians are two different units of measurement used to quantify angles in geometry and trigonometry.
Degrees
Degrees are the most common unit for measuring angles. A circle is divided into 360 degrees, and each degree is further divided into minutes (‘) and seconds (“). This system is widely used in everyday contexts, such as measuring angles in maps, navigation, and many day-to-day activities.
Radians
Radians are an alternative unit for measuring angles, particularly in mathematical calculations involving trigonometric functions. A radian is defined as the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle.
In a complete circle, there are 2π radians (approximately 6.283 radians). Radians are often preferred in advanced mathematics and physics because they simplify trigonometric formulas and calculations.
How to convert degrees to radians
To convert degrees to radians, you can use the following formula:
Radians = Degrees × (π / 180)
Here’s the step-by-step process:
- Take the angle measurement in degrees that you want to convert to radians.
- Multiply the degree measurement by π (pi).
- Divide the result by 180.
For example, let’s say you want to convert 45 degrees to radians:
Radians = 45 × (π / 180)
Radians = 0.25π
So, 45 degrees is approximately equal to 0.25π radians.
Degrees to radians conversion table
| Degrees (°) | Radians (rad) | Radians (rad) |
| 0° | 0 rad | 0 rad |
| 30° | π/6 rad | 0.5235987756 rad |
| 45° | π/4 rad | 0.7853981634 rad |
| 60° | π/3 rad | 1.0471975512 rad |
| 90° | π/2 rad | 1.5707963268 rad |
| 120° | 2π/3 rad | 2.0943951024 rad |
| 135° | 3π/4 rad | 2.3561944902 rad |
| 150° | 5π/6 rad | 2.6179938780 rad |
| 180° | π rad | 3.1415926536 rad |
| 270° | 3π/2 rad | 4.7123889804 rad |
| 360° | 2π rad | 6.2831853072 rad |
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FAQs on Degrees to radians
How do we convert degrees to radians?
To convert degrees to radians, you can use the formula: radians = degrees × (π / 180), where π (pi) is approximately 3.14159. Multiply the number of degrees by π divided by 180 to obtain the equivalent value in radians.
What is the formula for 1 radian to degrees?
The formula to convert radians to degrees is: degrees = radians × (180 / π). Multiply the number of radians by 180 divided by π to get the equivalent value in degrees.
What is the value of 1 degree in radians?
The value of 1 degree in radians is approximately 0.01745 radians. This is obtained by dividing π by 180.
How to convert 40 degrees 20 minutes into radian?
To convert degrees and minutes to radians, first convert the minutes to decimal form (divide minutes by 60), then follow the formula: radians = (degrees + decimal_minutes) × (π / 180). For example, to convert 40 degrees 20 minutes, first, convert 20 minutes to (20 / 60) = 0.3333 degrees. Then, calculate radians = (40 + 0.3333) × (π / 180).
What is 270 degrees in radians?
To convert 270 degrees to radians, use the formula: radians = degrees × (π / 180). Thus, radians = 270 × (π / 180), resulting in approximately 4.7124 radians.
How many radians is 180 degrees?
To convert 180 degrees to radians, apply the formula: radians = degrees × (π / 180). Therefore, radians = 180 × (π / 180), which equals π radians.
How do you convert 120 degrees to radians?
Convert 120 degrees to radians using the formula: radians = degrees × (π / 180). Thus, radians = 120 × (π / 180), yielding approximately 2.0944 radians.
