assume a,b starts on the positive x-axis and moves around in a circle. determine a function of a segment from the origin to a point a,b

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karton · Accepted Answer

To determine a function of a segment from the origin to a point A, B, where A and B move around in a circle starting on the positive x-axis, we can use the Pythagorean theorem.Let the angle that A makes with the positive x-axis be&amp;nbsp;θ. Then the coordinates of A are (a, 0), where a is the radius of the circle. The coordinates of B are&amp;nbsp;(acos(θ),asin(θ)), since B is a point on the circle with radius a and angle&amp;nbsp;θ.The distance from the origin to the point&amp;nbsp;(acos(θ),asin(θ))&amp;nbsp;is given by the Pythagorean theorem:d=(acos(θ))2+(asin(θ))2=a2cos2(θ)+a2sin2(θ)=a2(cos2(θ)+sin2(θ))=a2=aTherefore, the function that describes the distance from the origin to the point A, B is simply&amp;nbsp;f(θ)=a&amp;nbsp;for all values of&amp;nbsp;θ.

assume a,b starts on the positive x-axis and

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