1. 6.1.2 Angles

2. Converting to degrees Angles in radian measure do not always convert to angles in degrees without decimals, we must convert the decimal to minutes and seconds Example: 3 radians = 3 * 180 / pi = 171.8873 = 171° +.8873 * 60’ = 171° + 53.238’ = 171° + 53’ +.238*60” = 171° + 53’ + 14.28” = 171° + 53’ + 14”

3. Ex 2) 1.5 radians

4. Finding Arc length An arc is a piece of circle set between the two rays of an angle and the vertex of the angle is the center of the circle. This angle is known as a ARC

5. The Length of the Arc The length of the Arc is determined by the radius of the circle as well as the size of the angle First convert the angle (  ) measure to radians if it is not already The use the formula Arc Length = s =

6. Find the degree measure of the Central Angle s = 3ft r = 20in 381.972° = 

7. Area of a Circular Sector Circular Sector To find the area of the circular sector we must use a formula: A = Again we need to use  in radian measure

8. Find the Area of a Circular Sector with  = 120° and r = 9cm A = A = 27*pi cm 2

9. Angular and Linear Speed Angular Speed (radians per minute) = 2pi * RPM (revolutions per minute) Ex. A wheel spins at 350RPM Angular speed = 700pi (radians per minute) Linear speed = r * angular speed (units per minute) Ex. Wheel has radius 3 inches Linear speed = 2100pi in per minute

10. homework P. 401 17- 35 odd 37 a,e 38, 51