Question 148554: an equilateral triangle is inscribed in the circle of radius 1 centered at the origin (the unit circle). if one of the vertices is (1,0), what are the coordinates of the other two? The three points divide the circle into three arcs; what are the angular sizes of these arcs?
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! an equilateral triangle is inscribed in the circle of radius 1 centered at the origin (the unit circle). if one of the vertices is (1,0), what are the coordinates of the other two? The three points divide the circle into three arcs; what are the angular sizes of these arcs?
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The angles and arcs will be 360/3, or 120 degrees.
Draw the circle about the origin.
You can see that the point at 120 degs CCW from the point (1,0) has a negative x and a positive y component. The small angle between a line from the origin to the point is 60 degs.
So the distance on the x-axis is 1*cos(60) in the negative direction, or -0.5
The y value is +sin(60) = 0.866. The point is (-0.5,0.866)
The 2nd point is a reflection about the x-axis, or (-0.5,-0.866)
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