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6.1.2 Angles. Converting to degrees Angles in radian measure do not always convert to angles in degrees without decimals, we must convert the decimal.

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Presentation on theme: "6.1.2 Angles. Converting to degrees Angles in radian measure do not always convert to angles in degrees without decimals, we must convert the decimal."— Presentation transcript:

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


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