sin²(x)+cos²(x) = 1 isn't 𝑗𝑢𝑠𝑡 Pythagorean theorem on the unit circle It also tells us that a rotation (eⁱˣ) followed by its inverse rotation (e⁻ⁱˣ) is the same as no rotation at allpic.twitter.com/INSZcTxtXr
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Ok, but WHY these solutions are the circular functions (coordinate of the points on the circle)?
Because they satisfy the same differential equation with a unique solution. They must be. QED
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And HOW do you know this without knowing that the equation of the circle is x^2+y^2=1?
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I don’t get your point. All you need is the fact that they are equivalent, which you get from the ODE.
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