query: $\sin(ωt) + \sin(ωt+\Delta\theta) + \sin(ωt+2\,\Delta\theta) + \cdots + \sin(ωt+\overline{n-1}\,\Delta\theta) ={}$?
positive_passages.docid: 5080
positive_passages.text: How can we sum up $\sin$ and $\cos$ series when the angles are in arithmetic progression?
negative_passages.docid: 100907
negative_passages.text: $\sin\alpha + \sin\beta + \sin\gamma = 4\cos{\frac{\alpha}{2}}\cos{\frac{\beta}{2}}\cos{\frac{\gamma}{2}}$ when $\alpha + \beta + \gamma = \pi$
negative_passages.docid: 98570
negative_passages.text: Prove whether $f(n)$ is $O$, $o$, $\Omega$, $\omega$ or $\Theta$ of $g(n)$. $f(n) = n + (\log n)^{2}$, $g(n) = n + \log(n^{2})$.
negative_passages.docid: 77002
negative_passages.text: $\int_{0}^{\frac{\pi}{2}}\frac{d\theta}{a + \sin^2(\theta)} = \frac{\pi}{2\sqrt{a(a+1)}}$, for $a > 0$
negative_passages.docid: 17168
negative_passages.text: Find the value of $\sin\frac{2\pi}{7}+\sin\frac{4\pi}{7}+\sin\frac{8\pi}{7}$
negative_passages.docid: 154065
negative_passages.text: $\int_{\frac{1}{3}\pi}^{\frac{2}{3}\pi} {\sin(x)\;dx}$ using Riemann sums?
negative_passages.docid: 45227
negative_passages.text: If $\sin \theta+\cos\theta+\tan\theta+\cot\theta+\sec\theta+\csc\theta=7$, then $\sin 2\theta$ is a root of $x^2 -44x +36=0$ My own bonafide attempt.
negative_passages.docid: 60709
negative_passages.text: How do I get $\cos{\theta} \lt \frac{\sin{\theta}}{\theta} \lt 1$?
negative_passages.docid: 113675
negative_passages.text: Question about theta of $T(n)=4T(n/5)+n$
negative_passages.docid: 99328
negative_passages.text: Value of $\sin (2^\circ)\cdot \sin (4^\circ)\cdot \sin (6^\circ)\cdots \sin (90^\circ) $
negative_passages.docid: 42391
negative_passages.text: Calculate $\tan9^{\circ}-\tan27^{\circ}-\tan63^{\circ}+\tan81^{\circ}$
negative_passages.docid: 9539
negative_passages.text: $\alpha$ and $\beta$ are solution of $a \cdot \tan\theta + b \cdot \sec\theta = c$ show $ \tan(\alpha + \beta) = \frac{2ac}{a^2 - c^2}$
negative_passages.docid: 17102
negative_passages.text: If $\left(1+\sin \phi\right)\cdot \left(1+\cos \phi\right) = \frac{5}{4}\;,$ Then $\left(1-\sin \phi\right)\cdot \left(1-\cos \phi\right)$
negative_passages.docid: 85872
negative_passages.text: Prove $1 + \tan^2\theta = \sec^2\theta$
negative_passages.docid: 281
negative_passages.text: How one can prove $\prod_{k=1}^{n-1} (\cos\theta-\cos(k\pi/n)) = 2^{1-n}\sin(n\theta)\csc\theta$?
negative_passages.docid: 143200
negative_passages.text: $f(r,\theta)=(r\cos\theta,r\sin\theta)$ Then
negative_passages.docid: 112036
negative_passages.text: sum of series $\frac{n}{1\cdot 2 \cdot 3}+\frac{n-1}{2\cdot 3\cdot 4}+\frac{n-2}{3\cdot 4 \cdot 5}+\cdots \cdots n$ terms