Math127 Angles, Arc Length, and Circular Motion

Angle

A figure formed by two rays, called the sides of the angle, sharing a common endpoint known as the vertex.

Radian

A unit of angular measure equal to the angle subtended at the center of a circle by an arc equal in length to the radius of the circle.

Degrees

A unit of angle equal to 1/360 of a complete revolution.

Arc Length

The distance along the curved line making up the arc.

Arc Length Formula

The formula to calculate arc length is L = rθ, where L is arc length, r is radius, and θ is the angle in radians.

Sector Area

The region enclosed by two radii of a circle and the arc between them.

Area of Sector Formula

The formula for the area of a sector is A = 1/2 * r^2 * θ, where A is the area, r is the radius, and θ is the angle in radians.

Coterminal Angles

Angles that share the same terminal side but may differ in the amount of rotation.

Counterclockwise Angle

A positive angle measured from the initial side in a counterclockwise direction.

Negative Angle

An angle measured in the clockwise direction from the initial side.

Conversion from Degrees to Radians

To convert from degrees to radians, multiply the degree measure by π/180.

Conversion from Radians to Degrees

To convert from radians to degrees, multiply the radian measure by 180/π.

Standard Form of an Angle

An angle expressed as a radian measure that falls within the range of 0 to 2π.

Mixed Number (for angles)

A representation of an angle greater than 2π expressed as a whole number plus a fraction.

Quadrants

The four sections of the Cartesian coordinate plane, each defined by the signs of their x and y coordinates.