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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ODE arising from the properties of the goniometric functions (the double derivative of the sinus is - the sinus) and then we are back to step 1: Pythagorean theorem.
No. You define trig functions. You define properties of a complex exponential. Two separate worlds. They satisfy the same differential equations, which has a unique solution .
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Ok, but WHY these solutions are the circular functions (coordinate of the points on the circle)?
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Because they satisfy the same differential equation with a unique solution. They must be. QED
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