Final answer:
To find the arc length for a 60-degree central angle in a circle with a circumference of 6, we calculate one-sixth of the circumference, resulting in an arc length of 1 unit.
Step-by-step explanation:
The question is asking about the arc length of a circle given a circumference and a central angle. To find the arc length, also denoted as As, we use the formula that relates the arc length to the central angle and the radius of the circle (radius of curvature). If the entire circumference corresponds to a 360-degree angle, then a 60-degree angle would correspond to one-sixth of the circumference because 60/360 = 1/6. Here's the step-by-step calculation:
- The circumference (C) is 6, which means the entire circle represents a 360-degree rotation.
- Since there are 360 degrees in a full circle, a 60-degree angle corresponds to 60/360 or 1/6th of the full circle.
- Hence, the arc length for a 60-degree central angle is 1/6th of the circumference. So, As = C/6 = 6/6 = 1
Therefore, the length of the arc is 1 unit.