Chapter 4 Part 1

 Def: A radian is the measure of an angle that cuts off an arc length equal to the radius.  Radians ↔ Degrees ◦ One full circle = 360º = 2π radians ◦ One half circle = 180º = π radians  Decimal Degrees ↔ DMS ◦ One degree = 60 minutes (1º = 60’) ◦ One minute = 60 seconds (1’ = 60”) ◦ One degree = 60² or 3600 seconds (1º = 3600”)

 Standard Position ◦ Vertex ◦ Initial Side ◦ Terminal Side  Direction ◦ Positive angles ◦ Negative angles  Classification ◦ Quadrantal angles

 Complimentary angles  Supplementary angles

 Coterminal angles

 Arc Length  Sector Area  Angular Velocity  Linear Velocity

Quadrant I Ɵ = Ɵ ’ x y (x, y) Defintion: A reference angle is the smallest angle between the terminal side and the x-axis.

Quadrant II Ɵ = 180˚- Ɵ ’ x y (x, y) Defintion: A reference angle is the smallest angle between the terminal side and the x-axis. -x y (-x, y)

Quadrant III Ɵ = 180˚+ Ɵ ’ x y (x, y) Defintion: A reference angle is the smallest angle between the terminal side and the x-axis. -x -y (-x, -y)

Quadrant IV Ɵ = 360˚- Ɵ ’ x y (x, y) Defintion: A reference angle is the smallest angle between the terminal side and the x-axis. -y (x, -y)

Quadrant IV Ɵ = 360˚- Ɵ ’ (x, y) Defintion: A reference angle is the smallest angle between the terminal side and the x-axis. (x, -y) Quadrant III Ɵ = 180˚+ Ɵ ’ Quadrant II Ɵ = 180˚- Ɵ ’ Quadrant I Ɵ = Ɵ ’ (-x, -y) (-x, y)