Question 53918: When graphed using polar coordinates, the center of a regular nonagon is at the origin and one vertex is at (6,0 degrees) or (6,0 radians). Find the polar coordiantes of the other vertices in both degrees and radians.
Found 2 solutions by venugopalramana, AnlytcPhil:
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! When graphed using polar coordinates, the center of a regular nonagon is at the origin and one vertex is at (6,0 degrees) or (6,0 radians). Find the polar coordiantes of the other vertices in both degrees and radians.
regular nonagon has 9 equal sides and equal angles.each side subtends an angle of 360/9 = 40 degrees or 2pi/9 radians at centre.all vertices are at equal distance from centre.hence if we take the given vertex as A = (6,0)...it means r=6 and theta = 0
for all other vertices r will be same and theta will increase by 40 degrees each..hence
B = (6,40) in degres..............(6,2pi/9) in radians
C = (6,80).........................(6,4pi/9)
D = (6,120).........................(6,6pi/9)
E = (6,160).........................(6,8pi/9)
G = (6,200)..........................(6,10pi/9)
H = (6,240)...........................(6,12pi/9)
I = (6,280)...........................(6,14pi/9)
J = (6,320)............................(6,16pi/9)
Answer by AnlytcPhil(1806)  (Show Source):
You can put this solution on YOUR website! When graphed using polar coordinates, the center of a regular nonagon is at the
origin and one vertex is at (6,0 degrees) or (6,0 radians). Find the polar
coordiantes of the other vertices in both degrees and radians
The vertices of a nonagon are the enpoints of the "spokes" of a "9-spoke wheel",
each spoke measuring 6 units.
We divide 360° into 9 parts, 360°/9 = 40°. So the "spokes" are 40° apart, so
the vertices have as their second coordinates
0°, 40°, 80°, 120°, 160°, 200°, 240°, 280°, 320°
Each "spoke" is 6 units long, so the polar coordinates for the 9 vertices are
(6,0°), (6,40°), (6,80°), (6,120°), (6,160°), (6,200°), (6,240°), (6,280°), (6,320°)
In radians, 40° = 40(p/180) = 2p/9
So the polar coordinates in radians are:
(6,0), (6,2p/9), (6,4p/9), (6,6p/9), (6,8p/9), (6,10p/9), (6,12p/9), (6,14p/9), (6,16p/9)
Some of those fractions will reduce, so, after reducing those that will reduce
the vertices of the nonagon in radians are:
(6,0), (6,2p/9), (6,4p/9), (6,2p/3), (6,8p/9), (6,10p/9), (6,4p/3), (6,14p/9), (6,16p/9)
Edwin
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