1. Angles and Arcs
Lesson 2.1

2. Angles Ray Angle Formed of two rays Have same endpoint
Extends indefinitely
Ray
Angle
Formed of two rays
Have same endpoint
Endpoint

3. Angles Angles can be Straight Right Acute Obtuse Obese  less than 90°
greater than 90°
View NSpire Demo

4. Angles Positive Angles Negative Angles Measured counter-clockwise
Measured clockwise

5. Angles Degree = of a full revolution Complementary angles
a + b = 90°
Supplementary angles
a + b = 180°

6. Co-terminal Angles
We measure angles in standard position on the coordinate axes
This same angle could be θ

7. Radian Angle Measure
Consider the length of the radius laid out on the circumference
The resulting angle θ, is 1 radian
There are radians in a circle r θ r
View NSpire Demo

8. Radian Angle Measure Conversion of radians to degrees
Use this proportion
Solve for desired value (degrees or radians)
Try it:
is how many degrees?
135° is how many radians?

9. Arc Length Given a circle with radius r and central angle = θ radians
The arc length can be calculated by
Try it: For a circle with radius 3.5 and θ = what is the arc length? S θ r
View NSpire Demo

10. Linear and Angular Speed
Angular speed is radians/unit time
Linear speed is linear units / unit time

11. Linear and Angular Speed
If ω is the angular velocity of a round object with radius r
The linear velocity of a point on the circle is
For a 20 ft radius windmill rotating at 10 rpm, what is the linear velocity of the tip of the blade?

12. Assignment
Lesson 2.1
Page 130
Exercises 1 – 69 EOO 71,79,83