Final answer:
There are π/3 radians in 1/3 of a circle. To calculate these, we divide 2π, the angle in radians for a full circle, by 3.
Step-by-step explanation:
The student is asking how many radians are in 1/3 of a circle. Let's start by understanding that a full circle represents an angle of 2π radians.
Therefore, if we want to calculate the angle in radians for 1/3 of a circle, we can divide 2π by 3, which gives us π/3 radians. In a step-by-step explanation, we recognize that a full revolution, equating to 360°, is also equal to 2π radians, so to find 1/3 of this amount we simply take (1/3) × 2π.
This results in the equation (1/3) × 2π = (2π/3) radians. Simplifying this, we can see that 1/3 of a circle is equivalent to π/3 radians or approximately 2.0944 radians.