Arc length is the distance along the circumference of a circle or any other curved shape. It is important in mathematics because it allows us to measure the length of a curved line, which cannot be measured using traditional linear units.
The most common units used to measure arc length are degrees, radians, and the length of the radius. Degrees are based on dividing the circumference of a circle into 360 equal parts, while radians are based on dividing the circumference into 2π equal parts. The length of the radius is also commonly used to measure arc length in terms of the number of radii that make up the arc.
The formula for calculating arc length is L = rθ, where L is the arc length, r is the radius, and θ is the central angle in radians. If the angle is given in degrees, it must be converted to radians by multiplying by π/180 before plugging it into the formula.
A solved problem using arc length units would involve finding the length of a curved line or arc in a given shape, such as a circle or a segment of a circle. This would require using the formula L = rθ and plugging in the known values for the radius and central angle.
No, arc length cannot be negative. It is always a positive value representing the distance along the circumference of a circle or curved shape. If the calculated value is negative, it is likely due to an error in the calculation or a misunderstanding of the problem.