What is Arc in Math?
In mathematics, an arc is a segment of a curve, typically a part of the circumference of a circle or an ellipse. It is defined by two endpoints and all the points on the curve between them. The length of an arc is often measured in terms of the angle it subtends at the center of the circle or ellipse.
How to Make an Arc
To create an arc, follow these steps:
- Draw a Circle or Ellipse: Begin by drawing a circle or ellipse. Use a compass for accuracy if needed.
- Select the Arc Endpoints: Determine the two endpoints on the circumference of the circle or ellipse that will define the arc.
- Draw the Arc: Use a ruler or protractor to draw the arc, connecting the chosen endpoints.
Types of Arcs
Different types of arcs include minor arcs (covering less than half of the circle), major arcs (covering more than half), semicircles (exactly half), and central angle arcs (subtended by a central angle at the center).
Solved Examples
Example: Consider a circle with a radius of 5 cm. Find the length of the minor arc subtended by a central angle of 60 degrees.
Solution:
Therefore, the length of the minor arc is approximately 5.24 cm.