Angle Measure Lesson 6 1 n Angle Terminology

Angle Measure Lesson 6. 1

n Angle Terminology – Initial side – Terminal side – Vertex – Standard position 2

n Angle Terminology – Positive Angle • Counterclockwise – Negative Angle • Clockwise – Show positive/negative angles 3

n Angle Terminology – Coterminal • Share the same terminal side • Math Open Reference - Coterminal angles 4

Radian Measure To talk about trigonometric functions, it is helpful to move to a different system of angle measure, called radian measure n A radian is the measure of a central angle whose intercepted arc is equal in length to the radius of the circle. n Check out “What is a Radian? ” Also, for radian measure, does circle’s size matter? 5

How many radians in a circle? There are 2 radians in a full rotation -- once around the circle n There also 360° in a full rotation n 6

Radian Measure n There are 2 radians in a full rotation -once around the circle n There also 360° in a full rotation n To convert from degrees to radians or radians to degrees, use this conversion factor: 7

Sample Problems n Find the degree equivalent of radians: Find the radian measure equivalent of 210° : 8

n Radian – Degree comparisons 9

Uses of Radian Measure n Length of an intercepted arc: s = r 10

Uses of Radian Measure n Area of a sector: A = ½ r 2 11

Angular velocity vs. Linear Velocity – All skaters are moving at the same angular speed – All skaters are not moving at the same linear speed 12

Linear and Angular Speed n Linear speed is linear units / time: n Angular speed is radians / time: 13

n Angle Terminology – Coterminal • Share the same terminal side 14