Apr 16, 2021 · I will outline Euler's second proof of the Basel problem. If we start with the identity: $$ \frac {\sin (\pi x)} {\pi x}=\prod_ {n\geq 1}\left (1-\frac {x^2} { n^2 ...

Sep 27, 2023 · Using that I easily proved $\sin (\pi/6)=1/2$, But my doubt is, do the author wants the reader solve it using some sort of periodicity... is there any other method to prove it using the …

Sep 10, 2016 · I'm trying to demonstrate: $$ \\sin(π/6) = \\sin(30º) = 1/2 $$ Which property or assumption I should use to start?

Jun 9, 2014 · Why is $\\sin(30^\\circ)$ exactly $0.5,$ when it could be 0.49999 or something else? There must be an easy geometric explanation?

Aug 28, 2020 · The equation is cos(2x)cos(x− π 6)+sin(2x)sin(x− π 6) = 0 cos (2 x) cos (x π 6) + sin (2 x) sin (x π 6) = 0. This is same as cos(2x−(x− π 6)) = 0 cos (2 ...

Feb 17, 2019 · As has already been pointed, out, the absolute value is redundant since $\cos\frac {\pi} {6} > 0$ and since $\sqrt {x^2+y^2+z^2}$ is non-negative by definition of the square root function. But …

Sep 1, 2018 · The interval $\left (\frac {\pi} {6},\frac {\pi} {3}\right)$ is centered at $\frac {\pi} {4}$ and $\sin (x)+\cos (x)= \sqrt {2}\sin\left (x+\frac {\pi} {4}\right ...

It is slightly unfortunate that Khan Academy says Note: please answer in terms of radians (ex: "3/4 pi"), partly because whether $\pi$ is part of the denominator or not is unclear, and partly because it would …

May 20, 2022 · I dont want to criticize the validity of the result, but frankly the use of higher mathematics as a means to prove lower mathematics seems irrational and circular in reasoning. To respect the …

Mar 14, 2011 · Setting $\pi$ = 6.28 would seem to simplify many equations and constants in math and physics. Is there an intuitive reason we relate the circumference of a circle to its diameter instead of …