Question 603908: I need some help, no one has been able to answer this question.
A student is designing a club logo to be produced on a computer screen. The outline is a regular pentagon inscribed in a circle with radius 10. One vertex is at (0,10). Find (to the nearest thousandth) the coordinates of the other vertices.
Found 2 solutions by stanbon, scott8148:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A student is designing a club logo to be produced on a computer screen. The outline is a regular pentagon inscribed in a circle with radius 10. One vertex is at (0,10). Find (to the nearest thousandth) the coordinates of the other vertices.
10(cos(90 + (360b/5)) + i sin(90 + (360n/5))
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n = 0: 10(cos(90)+isin(90) = 0+10i
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n = 1: 10(cos(90+72)+ isin(90+72)) = -9.5106+3.0902i
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n = 2: 10(cos(90+2*72) + isin(90+2*72)) = -5.8779-8.0902i
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n = 3: 10(cos(90+3*72) + isin(90+3*72) = 5.8779+8.0902i
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n = 4: 10(cos(90+4*72) + isin(90+4*72) = 9.5106+3.0902i
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Each of those answers is in the form a + bi.
Those a,b values are the coordinates of the vertices of the pentagon.
Cheers,
Stan H.
Answer by scott8148(6628)  (Show Source):
You can put this solution on YOUR website! so the circle is centered at the origin, with the y-axis as an axis of symmetry for the pentagon
the other vertices are also 10 units from the origin
using radial notation (r,theta) ___ 360º / 5 = 72º
___ the given vertex is (10,90º)
___ the other vertices are ; (10,18º) , (10,162º) , (10,234º) , and (10,306º)
to convert to rectangular coordinates ___ y = r sin(theta) ; and x = r cos(theta)
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