Final answer:
An angle measuring 23π/18 radians represents 23/18 or about 1.2778 times the radian measure of a semicircle, making it slightly larger than a semicircle.
Step-by-step explanation:
To find what fraction of a semicircle an angle measuring 23π/18 radians represents, we first have to know the total radian measure of a semicircle. Since a full circle is 2π radians, a semicircle is half of that, which is π radians. To find the fraction of a semicircle represented by the angle 23π/18 radians, we divide the angle by π radians.
The calculation is as follows:
- θ(semicircle) = π radians
- θ(given angle) = 23π/18 radians
- Fraction of semicircle = θ(given angle) / θ(semicircle) = (23π/18) / π = 23/18
Therefore, an angle that measures 23π/18 radians is 23/18 or approximately 1.2778 times the radian measure of a semicircle. This means the given angle is slightly larger than a semicircle.