query: Solving $\sin x\cos3x+\cos x\sin3x=\frac{\sqrt{3}}{2}$ in the interval $[0, 2\pi]$. How to handle the interval?
positive_passages.docid: 142610
positive_passages.text: Solving $\sin x\cos3x+\cos x\sin3x=\sqrt{3}/2$ in the interval $[0,2\pi]$
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: 53438
negative_passages.text: I need assistance in integrating $ \frac{x \sin x}{1+(\cos x)^2}$
negative_passages.docid: 60275
negative_passages.text: calculation of $\int\frac{1}{\sin^3 x+\cos^3 x}dx$ and $\int\frac{1}{\sin^5 x+\cos^5x}dx$
negative_passages.docid: 46394
negative_passages.text: If $\frac{\cos \alpha}{\cos \beta}+\frac{\sin \alpha}{\sin \beta}=-1$, find $\frac{\cos^3\beta}{\cos \alpha}+\frac{\sin^3\beta}{\sin \alpha}$.
negative_passages.docid: 118701
negative_passages.text: Evaluate $\int_{0}^{\frac{\pi }{2}}\frac{x dx}{\sin x +\cos x}$
negative_passages.docid: 52018
negative_passages.text: Can $\frac{\sqrt{3}}{\sin20^{\circ}}-\frac{1}{\cos20^{\circ}}$ have two values?
negative_passages.docid: 38949
negative_passages.text: How to Evaluate $\int e^{2x}\sin(3x)\ dx$?
negative_passages.docid: 87489
negative_passages.text: Find range of $f(x)=3|\sin x|-4|\cos x|$
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: 30127
negative_passages.text: Integration of sqrt Sin x dx
negative_passages.docid: 125171
negative_passages.text: Help with this trigonometry problem?
negative_passages.docid: 28161
negative_passages.text: Solve $\lim_{x\to 0} \frac{\sin x-x}{x^3}$
negative_passages.docid: 99457
negative_passages.text: How to integrate $\int x\sin {(\sqrt{x})}\, dx$
negative_passages.docid: 61339
negative_passages.text: Integrating trigonometric function problem $\int \frac{3\sin x+2\cos x}{2\sin x+3\cos x}dx$
negative_passages.docid: 67340
negative_passages.text: Integrate $\int \frac{dx}{\sqrt{\sin^3x\sin(x+\alpha)}}$
negative_passages.docid: 90185
negative_passages.text: Another way to evaluate $\int\frac{\cos5x+\cos4x}{1-2\cos3x}{dx}$?