From 61b5ce20f25c5785e41574998a12c6d06eb05a5e Mon Sep 17 00:00:00 2001 From: Thomas Albers Date: Wed, 8 Mar 2023 23:43:00 +0100 Subject: Restructure build system and directory structures --- math/trigonometry.org | 51 --------------------------------------------------- 1 file changed, 51 deletions(-) delete mode 100644 math/trigonometry.org (limited to 'math/trigonometry.org') diff --git a/math/trigonometry.org b/math/trigonometry.org deleted file mode 100644 index 3e81eeb..0000000 --- a/math/trigonometry.org +++ /dev/null @@ -1,51 +0,0 @@ -#+TITLE:Trigonometric identities -#+SETUPFILE: ../math_options.org -#+LATEX_HEADER: \usepackage{bm} -#+LATEX_HEADER: \usepackage{mathtools} - -* Disclaimer -This site as of now just a technology demonstration and its claims -should not be taken as true (even though I myself am pretty confident -they are) - -* Pythagorean identities -\begin{align*} -&\cos^2\left(x\right) + \sin^2\left(x\right) = 1\\ -&\tan^2\left(x\right) + 1 = \sec^2\left(x\right)\\ -&1 + \cot^2\left(x\right) = \csc^2\left(x\right) -\end{align*} -* Sum of angles -\begin{align*} -&\sin\left(a \pm b\right) = \sin\left(a\right)\cos\left(b\right) \pm \cos\left(a\right)\sin\left(b\right)\\ -&\cos\left(a \pm b\right) = \cos\left(a\right)\cos\left(b\right) \mp \sin\left(a\right)\sin\left(b\right)\\ -&\tan(a \pm b) = \frac{\tan(a) \pm \tan(b)}{1 \mp \tan(a) \tan(b)} -\end{align*} -* Multiple angles -\begin{align*} -&\sin(2\theta) = 2\sin(\theta)\cos(\theta)\\ -&\cos(2\theta) = \cos^2\theta - \sin^2\theta = 2\cos^2\theta - 1 = 1 - 2\sin^2\theta -\end{align*} -* Half-angle formulae -\begin{align*} -&\sin \frac{\theta}{2} = \pm \sqrt{\frac{1-\cos\theta}{2}}\\ -&\cos \frac{\theta}{2} = \pm \sqrt{\frac{1+\cos\theta}{2}} -\end{align*} -* Power-reduction formulae -\begin{align*} -&\sin^2\theta = \frac{1 - \cos(2\theta)}{2}\\ -&\cos^2\theta = \frac{1 + \cos(2\theta)}{2} -\end{align*} -* Product-to-sum formulae -\begin{align*} -&2 \cos\theta \cos\varphi = \cos(\theta-\varphi) + \cos(\theta+\varphi)\\ -&2 \sin\theta \sin\varphi = \cos(\theta-\varphi) - \cos(\theta+\varphi)\\ -&2 \sin\theta \cos\varphi = \sin(\theta+\varphi) + \sin(\theta-\varphi)\\ -&2\cos\theta\sin\varphi = \sin(\theta+\varphi) - \sin(\theta-\varphi) -\end{align*} -* Sum-to-product formulae -\begin{align*} -&\sin\theta \pm \sin\varphi = 2 \sin\left(\frac{\theta\pm\varphi}{2}\right) \cos\left(\frac{\theta\mp\varphi}{2}\right)\\ -&\cos\theta + \cos\varphi = 2 \cos\left(\frac{\theta+\varphi}{2}\right) \cos\left(\frac{\theta-\varphi}{2}\right)\\ -&\tan\theta \pm \tan\varphi = \frac{\sin(\theta\pm\varphi)}{\cos\theta \cos\varphi}\\ -&\cos\theta - \cos\varphi = - 2 \sin\left(\frac{\theta+\varphi}{2}\right) \sin\left(\frac{\theta-\varphi}{2}\right) -\end{align*} -- cgit v1.2.3