query: Intuitive explanation of Euler's formula $e^{it}=\cos(t)+i\sin(t)$
positive_passages.docid: 742
positive_passages.text: How to prove Euler's formula: $e^{i\varphi}=\cos(\varphi) +i\sin(\varphi)$?
negative_passages.docid: 117583
negative_passages.text: Why does $\sum_{n=0}^\infty (\sin{\frac{1}{n}})(\sinh{\frac{1}{n}})(\cos n)$ converge
negative_passages.docid: 49044
negative_passages.text: Question about Eulers formula $v - e + f = 2$
negative_passages.docid: 84420
negative_passages.text: When is $\sin(x) = \cos(x)$?
negative_passages.docid: 147886
negative_passages.text: Proof of the angle sum identity for $\sin$
negative_passages.docid: 133905
negative_passages.text: Intuitive proof of $\sum_{k=1}^{n} \binom{n}{k} k^{k-1} (n-k)^{n-k} = n^n$
negative_passages.docid: 55095
negative_passages.text: Why can't we separate fraction powers in euler's formula?
negative_passages.docid: 6465
negative_passages.text: How to prove periodicity of $\sin(x)$ or $\cos(x)$ starting from the Taylor series expansion?
negative_passages.docid: 135302
negative_passages.text: Proof on Euler totient function
negative_passages.docid: 21203
negative_passages.text: An intuitive explanation of the Taylor expansion
negative_passages.docid: 149589
negative_passages.text: Analogous results to Euler's theorem
negative_passages.docid: 92205
negative_passages.text: Does Euler formula work for complex $z$?
negative_passages.docid: 107987
negative_passages.text: How do I calculate $u(w)=\int_0^\infty \frac{1-\cos(wt)}{t}\,e^{-t}\,dt$?
negative_passages.docid: 37040
negative_passages.text: Prove reduction formula for $\int \cos^n (x)\sin^m (x) \, dx$
negative_passages.docid: 109461
negative_passages.text: Solving equation involving Euler's totient function
negative_passages.docid: 125734
negative_passages.text: Has anyone talked themselves into understanding Euler's identity a bit?
negative_passages.docid: 137608
negative_passages.text: Proof of Euclid's formula for primitive Pythagorean Triples