6.1.2 angles. converting to degrees angles in radian measure do not always convert to angles in...
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6.1.2 Angles6.1.2 Angles6.1.2 Angles6.1.2 Angles
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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”
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Ex 2) 1.5 radians
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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
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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 =
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Find the degree measure of the Central
Angle• s = 3ft• r = 20in
• 381.972° =
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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
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Find the Area of a Circular Sector with = 120° and
r = 9cm• A =
• A = 27*pi cm2
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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
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homework• P. 401 17- 35 odd 37 a,e 38, 51