query: Evaluate $\cos \frac{\pi}{7} \cos \frac{2\pi}{7}\cos \frac{4\pi}{7}$
positive_passages.docid: 141816
positive_passages.text: factor $z^7-1$ into linear and quadratic factors and prove that $ \cos(\pi/7) \cdot\cos(2\pi/7) \cdot\cos(3\pi/7)=1/8$
negative_passages.docid: 26814
negative_passages.text: Solve $\int \frac{1}{\sin ^{\frac{1}{2}}x \cos^{\frac{7}{2}}x}dx$
negative_passages.docid: 136385
negative_passages.text: Integrate $ \int_{0}^{\frac{\pi}{4}}\tan^{-1}\left(\frac{\sqrt{2}\cos3 \phi}{\left(2\cos 2 \phi+ 3\right)\sqrt{\cos 2 \phi}}\right)d\phi$
negative_passages.docid: 138230
negative_passages.text: Evaluate $ \int^{\frac{\pi}{2}}_0 \frac{\sin x}{\sin x+\cos x}\,dx $ using substitution $t=\frac{\pi}{2}-x$
negative_passages.docid: 60709
negative_passages.text: How do I get $\cos{\theta} \lt \frac{\sin{\theta}}{\theta} \lt 1$?
negative_passages.docid: 105117
negative_passages.text: $1 + \frac{1}{3}\frac{1}{4} + \frac{1}{5}\frac{1}{4^2} + \frac{1}{7}\frac{1}{4^3} + ..........$
negative_passages.docid: 67322
negative_passages.text: evaluate $\int_{0}^{\infty}\cos(t) t^{z-1}dt=\Gamma(z)\cos(\frac{\pi z}{2})$
negative_passages.docid: 142114
negative_passages.text: Limit as $x\to 2$ of $\frac{\cos(\frac \pi x)}{x-2} $
negative_passages.docid: 122913
negative_passages.text: Evaluate $\int \frac{\sec^{2}{x}}{(\sec{x} + \tan{x})^{5/2}} \ \mathrm dx$
negative_passages.docid: 127129
negative_passages.text: Using the Argument Principle, evaluate $\int_{|z-i|=7}\frac{z\sinh(z)+3\cosh(z)z}{z\cosh(z)}dz$.
negative_passages.docid: 151063
negative_passages.text: Calculate $\int_{0}^{\frac{\pi}{2}}\frac{\sin^{3}(t)}{\sin^{3}(t)+\cos^{3}(t)}dt$ by hands
negative_passages.docid: 17188
negative_passages.text: Simplify $\cos(n \pi)$ and $\sin(n \pi)$ when n is an integer
negative_passages.docid: 71988
negative_passages.text: Evaluate $\int_0^{2\pi} \frac{\sin^2\theta}{5+4\cos\theta}\,\mathrm d\theta$
negative_passages.docid: 151563
negative_passages.text: Evaluate: $\int_{0}^{\pi}\frac{\cos 2017x}{5-4\cos x}dx$
negative_passages.docid: 146338
negative_passages.text: How to evaluate $\int\frac{1+x^4}{(1-x^4)^{3/2}}dx$?
negative_passages.docid: 27002
negative_passages.text: Evaluating $\int\limits_0^{\pi} \frac{dx}{1+2\sin^2x}$
negative_passages.docid: 131310
negative_passages.text: Evaluating $\dfrac{1}{\sin(2x)} + \dfrac{1}{\sin(4x)} + \dfrac{1}{\sin(8x)} + \dfrac{1}{\sin(16x)}$