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Published byRaymond Watson Modified over 9 years ago
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Circumference & Arc Length
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Circumference The distance around a circle C = 2r or d
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Ex: Find the circumference of a circle with a diameter of 12 cm. C = d C = (12) C = 12 C = 37.70 cm * If asked for an exact answer, the result would look like this. cm
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Ex: Find the radius of a circle with a circumference of 52 in. C = 2r 52 = 2r 52/2 = r 8.28 in. r
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Arc Length Arc Length is a PORTION of the circumference Don’t confuse arc length with arc measure The length of an arc is in linear units. (such as ft, cm, etc.) – it is dependent on the size of the circle The measure of an arc is in degrees (we have done this already at the beginning of the unit) – it is NOT dependent on the size of the circle
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Arc Length Percentage of the circle that your part is Will be in degrees
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Ex: Find the length of JK. ( C J K 60 o 16 in.
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Ex: Find the m LM. ( C L M 16.76 in. 8 i n. (
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Ex: Sometimes there are 2 steps - Find the length of LPM. ( C L M 100o 1 0 m P
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Ex: Find the radius C L M 125o P 5.7 cm
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Ex: Find the circumference of circle C. 45 o 10.2 cm R S C
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Radians Radians are another way to measure angles A radian is the ratio of the arc length to the radius
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Converting Radians 2π radians = 360 o Degrees = radians * 360/2 π Radians = degrees * 2 π/360
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Arc length with radians If we rearrange the formula for radians, it is easy to find arc length if given radians
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Examples Convert to radians Convert to degrees If an angle has a measure of π radians and the radius of the circle is 8 inches, what is the arc length?
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