Lesson 4.1 Radian & Degree Measure

Lesson 4.1Radian & Degree Measure

Parts and Types of AnglesTerminal & Initial Positive & Negative

Coterminal

A positive and negative angle where

on360

30o & ______

120o & ______

Investigate1. Draw a circle and make up a number for the radius.

2. Estimate a sector where the arc length would be equal to the radius

3. Find the circumference of the circle.

4. Use the formula below to find the degree measure of the arc

5. Then, what is the measure of the central angle of your sector?

6. Write your results in the table:

oangle ncecircumfere

lengtharcmARC 360_

radius

Circ.

mARC

angle

RadianThe angle size when the arc length equals the radius of a circle

Full revolution:

2rs

rs 2

rado _2360

rado _180

rad_2

Question: How many radians to equal 180o? 360o?

Radian MeasuresThe units of an angle are in degrees or radians

orad180

deg

o

rad 180deg Units haveto cancel

Converting

Examples

Sketch in standard position.

Find 2 coterminal angles to

Arc Length and Speed

rs Arc Length =

Linear Speed =ts

Angular Speed = t

Speed = Distance over time

Units = radians

Example

Find the angle in degrees

31 in.

12 in.𝜃