query: Show $\sin(z)=w$ can be solved $\forall w\in\Bbb C$
positive_passages.docid: 144188
positive_passages.text: Prove that $\cos(z)$ and $\sin(z)$ are surjective over the complex numbers.
negative_passages.docid: 31575
negative_passages.text: Solving trigonometric equations of the form $a\sin x + b\cos x = c$
negative_passages.docid: 55673
negative_passages.text: Alternate proof that $\exists\ x \in \Bbb{Z}$ such that $ \gcd (a+bx,c) = 1$?
negative_passages.docid: 149634
negative_passages.text: $ 2|f^{'}(0)| = \sup_{z, w \in D} |f(z)-f(w)|$
negative_passages.docid: 105487
negative_passages.text: Prove that $\sin x \cdot \sin (2x) \cdot \sin(3x) < \tfrac{9}{16}$ for all $x$
negative_passages.docid: 141273
negative_passages.text: When is $\sin(x)$ rational?
negative_passages.docid: 57152
negative_passages.text: Solve $\sin x = 1 - x$
negative_passages.docid: 16704
negative_passages.text: $\frac{1}{z}-\frac{1}{\sin z}$ at the origin - Classify singularities
negative_passages.docid: 48038
negative_passages.text: If $z$ and $w$ are complex numbers such that $|(z+w)| = |(z-w)|$, prove that $\arg(z)-\arg(w) = \pm (\pi/2)$
negative_passages.docid: 149447
negative_passages.text: Proving $\sin (x)=\cos (90^\circ-x)$
negative_passages.docid: 79808
negative_passages.text: Prove the representation of complex numbers is parallelogram
negative_passages.docid: 123136
negative_passages.text: Proof of the identity: $c\sin \frac{A-B}{2} \equiv (a-b) \cos \frac{C}{2}$
negative_passages.docid: 147886
negative_passages.text: Proof of the angle sum identity for $\sin$
negative_passages.docid: 15300
negative_passages.text: How to show that $(W^\bot)^\bot=W$ (in a finite dimensional vector space)
negative_passages.docid: 91744
negative_passages.text: Proving sum of sines is periodic when ratio of their frequencies is rational using differentation
negative_passages.docid: 94425
negative_passages.text: What is $\sup(\sin(n))$?
negative_passages.docid: 24585
negative_passages.text: Proving that $\mathbf{W}$+$\mathbf{W^{\perp}}$=$\mathbb{R^{n}}$