6.1 Angles and Their Measure

Trigonometry

Measurement of triangles

Angle

Rotating a ray (half-line) about its endpoint

Initial Side

The starting position of the ray

Terminal Side

The ending position of an angle that has been rotated from its initial side

Vertex

Endpoint of the ray

Standard Postion

Counter Clockwise Rotation

Positive angles

Clockwise Rotation

Negative angles

Coterminal Angles

Angles in standard position that share the same terminal side, meaning they point in the same direction

Measure of an Angle

The amount of rotation from the initial side to the terminal side

Degree

Common unit of angle measure

Unit Circle

Quadrantal Angle

An angle in standard position whose terminal side lies on one of the coordinate axes

Quadrants

.

Complementary and Supplementary Angles 

Complementary - When their sum is 90 degrees

Supplementary - When their sum is 180 degrees

Radian Measure

Central angle of a circle, which is an angle whose vertex is the center of the circle

One Radian

Measure of a central angle that intercepts an arc equal in length to the radius of the circle

Radian Measure Formula / Arc Length

Degrees to radians

Radians to Degrees

Angular Speed

Angular speed measures how fast the angle changes

Linear Speed

Linear speed measures how fast the particle moves

Sector

Region bounded by two radii of the circle and their intercepted arc

Area of a Sector of a Circle