CONCEPT PREVIEW Find the exact length of each arc intercepted by the given central angle. ​​

Key Concepts

Central Angle

A central angle is an angle whose vertex is at the center of a circle and whose sides (rays) extend to the circumference. The measure of a central angle is directly related to the arc it intercepts, meaning that the angle helps determine the length of the arc. In trigonometry, understanding central angles is crucial for calculating arc lengths and other properties of circles.

Arc Length Formula

The arc length of a circle can be calculated using the formula: Arc Length = r * θ, where 'r' is the radius of the circle and 'θ' is the central angle in radians. This formula shows the direct relationship between the radius, the angle, and the length of the arc. Converting degrees to radians may be necessary when using this formula, as it is commonly expressed in radians.

Radians and Degrees

Radians and degrees are two units for measuring angles. One complete revolution (360 degrees) is equivalent to 2π radians. Understanding how to convert between these two units is essential for solving problems involving angles in trigonometry, especially when applying formulas like the arc length formula, which typically requires angles to be in radians.