4.2 Degrees and Radians

Vertex

2 noncollinear rays that share a common endpoint

Sector

A region bounded by a central angle and it's intercepted arc.

Standard Position

An angle with its vertex at the origin and it's initial side along the positive x-axis is said to be in standard position.

Coterminal angles

By defining angles in terms of their rotation about a vertex, two angles can have te same initial and terminal sides but different measures.

Arc length

If (theta) is a central angle in a circle of radius "r" then the length of the intercepted arc is given by S=r(theta) where theta is measured in radians.

Area of a sector

The area A of a sector of a circle with radius "r" and central angle theta is A= 1/2(r)^2(theta)

Radiance measure

The measure (theta) in radians of a central angle of a circle is equal to the ratio of the length of the intercepted arc "s" to the radius "r" of the circle.

Linear speed

The rate at which an object moves along a circular path V=s/t

Angular Speed

The rate at which the object ROTATES about a fixed point W = ø/t

Terminal Side

The ray's position after rotation forms the angle's terminal side.

Initial side

The starting position of the ray forms the initial side of an angle

Degree/radian conversion rules

To convert a degree measure to radians, multiply by: pi raidians/180 To convert a radian measure to degrees, multiply by 180/pi radians