13-3: Radian Measure Radian Measure There are 360º in a circle The circumference of a circle = 2r. So if the radius of a circle were 1, then there a.

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Presentation transcript:

13-3: Radian Measure Radian Measure There are 360º in a circle The circumference of a circle = 2r. So if the radius of a circle were 1, then there a circle would contain 2 radians. This gives us our conversion factor: 360º = 2 radians Note: Dividing both sides by 2 gives: 180º =  radians 1 revolution around a circle = 2 radians 3 / 4 revolution: 3 / 4 * 2 = 3 / 2 radians 1 / 2 revolution: 1 / 2 * 2 =  radians 1 / 4 revolution: 1 / 4 * 2 =  / 2 radians 2 ½ revolutions = 2 ½ * 2 = 5 radians

13-3: Radian Measure Converting Between Degree and Radians Use the conversion factor:  = 180° (or 2  = 360°) Convert the following degree measurements to radians 75° 75° *  / 180° = 75  / 180 = 5  / ° 220° *  / 180° = 220  / 180 = 11  / 9 400° 400° *  / 180° = 400  / 180 = 20  / 9

Converting Between Degree and Radians Use the conversion factor:  = 180° (or 2  = 360°) Convert the following radian measurements to degrees  / 5  / 5 * 180° /  = 180 / 5 = 36° 4  / 9 4  / 9 * 180° /  = 720 / 9 = 80° 6  6  * 180° /  = 1080°

Arc Length An arc with central angle measure θ radians has length: l = r θ The arc length is the radius times the radian measure of the central angle of the arc. Example Find the length of arc s l = 3  5  / 6 = 5  / 2  7.9 inches Find the length of arc b l = 3  2  / 3 = 2   6.3 inches

Assignment Page 729 – 730 Problems 1 – 13, 21 – 25 (odd) For problem 13, just write all the equivalent statements (don’t worry about drawing the circle, though you can)