1. 4.1 Radian and Degree measure
Changing Degrees to Radians
Linear speed
Angular speed

2. Definition of an angle
An angle is made from two rays with a common initial point.
In standard position the initial side is on the x axis

3. Positive angle vs. Negative angle
Positive angles are Counter clockwise C.C.W.
Negative angles are Clockwise C.W.

4. Angles with the same initial side and terminal side are coterminal.

6. The measure of an angle is from initial side to terminal side
Vertex at the origin (Center)

7. Definition of a Radian
Radian is the measure of the arc of a unit circle.
Unit circle is a circle with a radius of 1.

8. The quadrants in terms of Radians
What is the circumference of a circle with radius 1?

9. The quadrants in terms of Radians
What is the circumference of a circle with radius 1?

10. The quadrants in terms of Radians
The circumference can be cut into parts.

11. The quadrants in terms of Radians
The circumference can be cut into parts.

12. Find the Coterminal Angle
Since equals 0. it can be added or subtracted from any angle to find a coterminal angle.
Given

13. Radian vs. Degree measurements
360º =
180º =
So or

14. Radian vs. Degree measurements
360º =
180º =
So or
To convert Degrees into Radians multiply by
To convert Radians into Degrees multiply by

15. Change 140º to Radians Change to degrees
Use degree to rads.
Use rads to degrees

16. How to use radian to find Arc length
The geometry way was to find the circumference of the circle and multiply by the fraction. Central angle
360º
In degrees Are length called S would be

17. How to use radian to find Arc length
In degrees Are length called S would be
In radian the equation is

18. r = 9, θ = 215º Changing to rads
Are length S

19. Linear speed and Angular speed
Linear speed is
Angular speed is
Assuming “constant speed”

20. Homework
4.1
11,12,15,17,29,25,29,31,35,37-39,43,47,49,51,53,55,57,63,64,69