William W. answered • 05/21/20
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The arc length equation is s = rθ where "s" is the arc length, "r" is the radius of the circle, and "θ" is the central angle in radians (not degrees).
In this case, since it is the unit circle, r = 1
So s = (1)(9π/2) = 9π/2
William W.
I think you are making it harder than it is David. The angle is more than 1 revolution but it’s still the length of the arc subtended by the angle.
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05/23/20
David M.
HOWEVER: The angles 9(π/2) and π/2 end up at the same place on the unit circle. Is the angle intercepted on a unit circle understood to be the shortest arc, from the positive part of the x axis, in which case the answer is (π/2); or does one take into account the full distance that the angle passes through to get to 9(π/2), in which case the answer is 9(π/2)? This is a detail I don't remember being confronted with. As an instructional to the ASKER of the QUESTION: The formula s = rθ, when working in radians, comes from the fraction of the arc length, s, to the circumference of a circle (2πr) being proportional to the fraction of the angle, θ, to a full circle, 2π. So, s/(2πr)=θ/(2π) Multiplying both sides of the equation by (2πr) s=(2πr)θ/(2π) s-rθ If we were working in degrees, 9π/2=810deg s/(2πr)=θ/(360) s=(2πr)θ/(360) s=rθ(π/180)05/23/20