Angle Conversion: Radians to Percentage
The question asks to find what percentage of a full circle is represented by an angle of $\frac{\pi}{2}$ radians.
Understanding Circle Measurements
- A full circle measures $360^\circ\) in degrees.
- A full circle measures $2\pi\) radians.
Calculation Steps
To find the percentage, we calculate the ratio of the given angle to the angle of a full circle and multiply by 100%.
- Identify the given angle: The angle is $\frac{\pi}{2}\) radians.
- Identify the angle of a full circle in radians: A full circle is $2\pi\) radians.
- Calculate the ratio: $ \text{Ratio} = \frac{\text{Given Angle}}{\text{Full Circle Angle}} = \frac{\frac{\pi}{2}}{2\pi} $
- Simplify the ratio: $ \frac{\frac{\pi}{2}}{2\pi} = \frac{\pi}{2} \times \frac{1}{2\pi} = \frac{\pi}{2\pi \times 2} = \frac{1}{4} $
- Convert the ratio to a percentage: $ \text{Percentage} = \text{Ratio} \times 100\% = \frac{1}{4} \times 100\% = 25\% $
Result
An angle of $\frac{\pi}{2}\) radians represents 25% of a full circle.
Similar Questions
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