anonymous
  • anonymous
When I draw a circle with a compass, then keeping that same angle with the compass, I can draw 6 equal segments along the circumference of the circle. Why is 1 radian not equal to 60 degrees?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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Mertsj
  • Mertsj
Because 1 radian is defined as the measure of the central angle that subtends an arc that is equal to the radius.
Mertsj
  • Mertsj
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Mertsj
  • Mertsj
You see, the chord is equal to the radius, not the arc.

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anonymous
  • anonymous
I still don't understand.... When the marks are made along the circumference of the circle with the compass set at the length of the radius, the length of the chord is the length of the radius. The needle and the pencil measure in a straight line, not an arc.
Mertsj
  • Mertsj
The arc is NOT equal to the radius!!! The chord is.
anonymous
  • anonymous
That is what I said.
Mertsj
  • Mertsj
|dw:1377919052063:dw|
Mertsj
  • Mertsj
Which is longer? Arc AB or chord AB?
anonymous
  • anonymous
Obviously the arc is longer. I know that. My point is that the marks made with the compass measure the chord and not the arc.
Mertsj
  • Mertsj
So you have answered your own question. Good for you.
anonymous
  • anonymous
I don't think we understand each other. Could you point me to some references instead?
Mertsj
  • Mertsj
|dw:1377919375606:dw|
anonymous
  • anonymous
You said the chord was equal to the radius. This picture indicates that the arc is equal to the radius. If it is the arc (and not the chord) that equals the radius, that makes more sense.
anonymous
  • anonymous
Soooo...According to Wikipedia, the length of the radius is equal to the length of the arc. That explains the reason for a full circle measuring \(2\pi\) radians since the circumference of the circle equals \(2\pi\). Which as I look back to the beginning is what Mertsj said in the first statement and the last image.

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