Monday, June 11, 2007

Arc length

>Practice Problems

a) At a central angle of 2.35 radians, what ratio has the arc to the radius?
b) In which quadrant of the circle does 2.35 radians fall?
c) If the radius is 10 cm, and the central angle is 2.35 radians, then how long is the arc?

*****ANSWERS ARE IN COMMENTS!!**********


Problem 1
a) At a central angle of π /5, approximately what ratio has the arc to the radius? Take π=3.
b) If the radius is 15 cm, approximately how long is the arc?
Problem 2
In a circle whose radius is 4 cm, find the arc length intercepted by each of these angles. Again, take π = 3.
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1 comment:

mpooh said...

Answers.
a)That number is the ratio. The arc is 2.35 times the radius.
b)Since π = 3.14, then π/2 is half of that : 1.57.
3π/2 = 3.14 +1.57 = 4.71
An angle of 2.35 radians, then, is greater than 1.57 but less that 3.14. It falls in the second quadrant.
c) s = r θ
s = 10 × 2.35
= 23.5 cm

Answers
Problem 1
a) The radian measure of π /5 is the same ratio. So if we take that π=3, then the ratio is 3/5 of the radius.
b) s = 15(3 /5)
= 9 cm.
Problem 2
a) π/4
s = rθ
=4· ¾
= 3 cm.

b) π/6
s = rθ
=4· 3/6
= 4· ½
= 2 cm

c)3π/2
s = rθ
= 4· (3·3/2)
= 4 · (9/ 2)
= 18 cm.

d) 2π. (Here, the arc length is the entire circumference!)
S = rθ
= 4· 2π
=4· 6
= 24 cm

June 11, 2007 at 10:40 AM

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