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[2024/05/06] Equation of circle (lemmy.world)

submitted 4 months ago* (last edited 4 months ago) by [email protected] to c/[email protected]

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Show that arcsin y = arccos x is the equation of a circle.
Note that the equation of a circle is x^2+y^2=1.

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[–] [email protected] 4 points 4 months ago

solution

arcsin(y) = arccos(x) implies y = sin(arccos(x))

sin(arccos(x)) can be shown to equal ±sqrt(1-x²) with a simple triangle diagram and the pythagorean theorem, so we have y = ±sqrt(1-x²). This can be easily re-arranged to give x² + y² = 1.