1. 6.3 Angles and Radian Measure

2. Parts of an Angle
Modern trigonometry is based around the thought that an angle is formed by rotating a ray around its endpoint.
Vertex: the endpoint of the angle
Initial side: starting position of the ray
Terminal side: the final position after the rotation

3. Terminal
40⁰
Vertex
Initial
Initial
Vertex
-43⁰
Terminal
Terminal
830⁰
Vertex
Initial

4. Positioning of an Angle
An angle in the coordinate plane is said to be in standard position if its vertex is at the origin and its initial side is on the positive x-axis.
Negative angle
Positive angle

5. Coterminal Angles
Angles formed by different rotations that have the same initial and terminal sides are called coterminal.
Ex. Find three angles coterminal with an angle of 60⁰ in standard position.
60⁰ + 360⁰ =
60⁰ - 360⁰ =
60⁰ + 2(360⁰) =