Expert: Sherman D. - 6/22/2009

Question
Express each angle in degrees :

1.   7π_
         2


2.   8π_
         5

3.   11π_
       15


Express each angle in radians ; leave in terms of π radians.

4.   144°


5.   225°


6.   15°



Find the length of the arc intercepted by the given angle :

7.   Circle of radius 20 cm ;  angle  2π/3


8.   circle of radius 12 inches ;  angle  3π/5


9.   circle of radius  48 cm  ;  angle 11π/12  

Answer
Write it like this

when going from pi to degrees, just replace pi with 180.

1.) (7pi)/2 or (7/2)pi = 630° or 270°

2.) (8/5)pi = 288°

3.) (11/15)pi = 132°

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Express each angle in radians ; leave in terms of π radians.

When going from degrees to pi, just divide the degrees by 180 and put pi onto it.

4.) 144° = 144/180 = (4/5)pi

5.) 225° = (5/4)pi

6.) 15° = pi/12

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Find the length of the arc intercepted by the given angle :

7. Circle of radius 20 cm ;  angle  2π/3

s = 20(2pi/3) = about 41.89cm

8. circle of radius 12 inches ;  angle  3π/5
s = 12(3pi/5) = about 22.62 inches


9. circle of radius  48 cm  ;  angle 11π/12
s = 48(11pi/12) = about 138.23 cm

http://mathforum.org/dr.math/faq/formulas/faq.circle.html#arc