query: How to express $\cos\left(\frac{\theta}{3}\right)$ in terms of $\cos(\theta)$?
positive_passages.docid: 148207
positive_passages.text: Express $\cos 6\theta $ in terms of $\cos \theta$
negative_passages.docid: 27910
negative_passages.text: How to evaluate $\int_0^{2\pi} \frac{d\theta}{A+B\cos\theta}$?
negative_passages.docid: 14279
negative_passages.text: Indefinite Integral with "sin" and "cos": $\int\frac{3\sin(x) + 2\cos(x)}{2\sin(x) + 3\cos(x)} \; dx $
negative_passages.docid: 24311
negative_passages.text: Proving $\frac{\sin x}{x} =\left(1-\frac{x^2}{\pi^2}\right)\left(1-\frac{x^2}{2^2\pi^2}\right) \left(1-\frac{x^2}{3^2\pi^2}\right)\cdots$
negative_passages.docid: 60230
negative_passages.text: Prove that $\frac{1+\sin\theta+i\cos\theta}{1+\sin\theta-i\cos\theta}=\sin\theta+i\cos\theta$
negative_passages.docid: 36586
negative_passages.text: Evaluating $\frac{1}{2\pi}\int_{0}^{2\pi}\frac{1}{1-2t\cos\theta +t^2}d\theta$
negative_passages.docid: 63679
negative_passages.text: Picture/intuitive proof of $\cos(3 \theta) = 4 \cos^3(\theta)-3\cos(\theta)$?
negative_passages.docid: 617
negative_passages.text: Find θ: $β=\arctan\frac{(R+r)·\sin(θ)-r·\sin(θ(1+\frac{R}{r}))}{(R+r)·\cos(θ)-r·\cos(θ(1+\frac{R}{r}))}$
negative_passages.docid: 29190
negative_passages.text: $\left\lfloor \frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{4}}+...+\frac{1}{\sqrt{1024}}\right\rfloor =?$
negative_passages.docid: 40235
negative_passages.text: How would I differentiate $\sin{x}^{\cos{x}}?$
negative_passages.docid: 126236
negative_passages.text: General closed form of $\int_{0}^{\theta_0} \frac{1}{\sqrt{\cos \theta-\cos \theta_0}} d\theta$
negative_passages.docid: 24656
negative_passages.text: Proving that $\frac{\csc\theta}{\cot\theta}-\frac{\cot\theta}{\csc\theta}=\tan\theta\sin\theta$
negative_passages.docid: 127380
negative_passages.text: Use vectors to prove $\cos(\beta - \alpha) = \cos \alpha \cos\beta + \sin\alpha \sin\beta$
negative_passages.docid: 49999
negative_passages.text: Express $y$ from $\ln(x)+3\ln(y) = y$
negative_passages.docid: 17769
negative_passages.text: Show that $\frac{\sin x}{\cos 3x}+\frac{\sin 3x}{\cos 9x}+\frac{\sin 9x}{\cos 27x} = \frac{1}{2}\left(\tan 27x-\tan x\right)$
negative_passages.docid: 129443
negative_passages.text: $f(\theta) = \cos \theta - \sqrt{3}\sin \theta$ in the form $r\sin(\theta-\alpha)$
negative_passages.docid: 77978
negative_passages.text: Show that $\frac {\sin x} {\cos 3x} + \frac {\sin 3x} {\cos 9x} + \frac {\sin 9x} {\cos 27x} = \frac 12 (\tan 27x - \tan x)$