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There is no logic for degrees. The degrees of a circle were arbitrarily chosen to be 360, probably because of the magic number 12 (used also in seconds, hours, months, dozen, etc.)

The logic of radians is that the circumference of a circle is 2 pi r, therefor the radians of a circle is 2 pi, making calculations easy.

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Q: What is the logic behind the degree and radians?
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