Final answer:
To convert a fraction to radians, multiply the fraction by π/180. This method is based on the relationship of π radians to 180 degrees. The correct answer is A.
Step-by-step explanation:
To convert a fraction to radians, you should multiply the fraction by π/180. This is because there are π radians in 180 degrees, which is half a revolution or circle. The fraction represents a degree value, and multiplying it by π/180 converts it into its equivalent radian measure.
Here is a step-by-step explanation for converting a fraction of degrees to radians:
- Start with the fraction that represents the angle in degrees.
- Multiply this fraction by π/180. This conversion factor is derived from the relationship that 2π radians equal 360 degrees (a full revolution), so π radians equal 180 degrees, and thus the conversion factor becomes π/180 to convert from degrees to radians.
- The result of this multiplication will give you the angle in radians.
- Remember to simplify the resulting expression if possible.
For example, to convert 3/4 degrees to radians:
- Take the fraction ⅔ (which is 0.75 degrees).
- Multiply by π/180: ⅔ * (π/180) = 0.75π/180.
- Simplify to get the answer in radians: (0.75π/180) = π/240 radians.
After obtaining the result, it's important to check if the answer is reasonable. If the original angle in degrees was a small fraction, the result in radians should also be relatively small since radians and degrees are both units that measure angles.