1. Notes 4.1 – Angles and Their Measure

2. I. Angle Measure
Each degree is divided into 60 minutes and each minute is divided into 60 seconds

3. B.) Ex.- Convert 65.875º to DMS (Degrees/Minutes/Seconds)

4. C.) Ex.- Convert 135º 28’ 42’’ to decimal degrees.

5. II. Course and Bearing
A.) Def: The angle, measured clockwise, between due North and the line of travel
B.) Graphically:

6. III. Radian Measure
A.) Def: A central angle of a circle has a measure of 1 RADIAN if it intercepts an arc with the same length as the radius. a

7. B.) Conversions:
1.) Radians to degrees :
2.) Degrees to radians :

8. C.) Ex.- Convert the following degree measures to radians.

9. D.) Ex.- Convert the following degree measures to radians.

10. IV. Arc Length
A.) Def: If θ is a central angle of a circle with radius r and θ is measured in radians, then the arc length s is given by
B.) If θ is in degrees:

11. C.) Ex.- Find the perimeter of a slice pizza from a large pie (8 slices) if it has an 8 inch radius.

12. V. Linear Motion A.) Angular speed = revolutions per minute
B.) Linear speed = miles per hour
1 radian = 1 radius

13. C. ) Ex. Find the speed of a truck with wheels 36 in
C.) Ex. Find the speed of a truck with wheels 36 in. in diameter that are rotating at 630 rpm (revolutions per minute).

14. VI. Statute vs. Nautical Miles
1 Statute mile ≈ Nautical mile
1 Nautical mile ≈ Statute miles