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

Answered question

2022-03-21

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

Answer & Explanation

karton

karton

Expert2023-04-25Added 613 answers

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 θ. Then the coordinates of A are (a, 0), where a is the radius of the circle. The coordinates of B are (acos(θ),asin(θ)), since B is a point on the circle with radius a and angle θ.

The distance from the origin to the point (acos(θ),asin(θ)) is given by the Pythagorean theorem:

d=(acos(θ))2+(asin(θ))2
=a2cos2(θ)+a2sin2(θ)
=a2(cos2(θ)+sin2(θ))
=a2
=a

Therefore, the function that describes the distance from the origin to the point A, B is simply f(θ)=a for all values of θ.

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