6.1.2 Angles6.1.2 Angles6.1.2 Angles6.1.2 Angles

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”

Ex 2) 1.5 radians

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

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 =

Find the degree measure of the Central

Angle• s = 3ft• r = 20in

• 381.972° =

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

Find the Area of a Circular Sector with = 120° and

r = 9cm• A =

• A = 27*pi cm2

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

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