- Show that
arcsin y = arccos xis the equation of a circle. - Note that the equation of a circle is
x^2+y^2=1.
The text below the image is wrong. It should state arcsin(y) = arccos(x)
this post was submitted on 07 May 2024
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mb, its now fixed
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.
Solution (that is likely much better than yours): https://gmtex.siri.sh/fs/1/School/Extra/Maths/Qotd%20solutions/2024-05-06_equation-of-circle.html
spoiler
::: spoiler spoiler
sin^2 (x) + cos^2 (x) = 1