diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json index c7ede01..9c6290c 100644 --- a/.obsidian/workspace.json +++ b/.obsidian/workspace.json @@ -90,9 +90,23 @@ "icon": "lucide-file", "title": "Trigonometri" } + }, + { + "id": "fc32ad4cc63e1ba9", + "type": "leaf", + "state": { + "type": "split-diff-view", + "state": { + "aFile": ".obsidian/workspace.json", + "bFile": ".obsidian/workspace.json", + "aRef": "" + }, + "icon": "diff", + "title": "Diff: workspace.json" + } } ], - "currentTab": 5 + "currentTab": 4 } ], "direction": "vertical" @@ -149,7 +163,8 @@ } ], "direction": "horizontal", - "width": 300 + "width": 300, + "collapsed": true }, "right": { "id": "b700e0cd0f882a5c", @@ -213,13 +228,13 @@ "state": { "type": "outline", "state": { - "file": "Grafer.md", + "file": "Komplexa tal.md", "followCursor": false, "showSearch": false, "searchQuery": "" }, "icon": "lucide-list", - "title": "Outline of Grafer" + "title": "Outline of Komplexa tal" } }, { @@ -237,7 +252,7 @@ } ], "direction": "horizontal", - "width": 200 + "width": 343 }, "left-ribbon": { "hiddenItems": { @@ -251,15 +266,16 @@ "obsidian-git:Open Git source control": false } }, - "active": "76c8d943958d45bf", + "active": "e616c86f78b96cf1", "lastOpenFiles": [ + "Trigonometri.md", + "Komplexa tal.md", "Gräsvärde (1).md", + "conflict-files-obsidian-git.md", "gv1.png", "Funktioner.md", "Funktioner Forts.md", - "Komplexa tal.md", "Grafer.md", - "Trigonometri.md", "k2.png", "k1.png", "f_inverse.png", diff --git a/Trigonometri.md b/Trigonometri.md index 44b1dac..8fb2176 100644 --- a/Trigonometri.md +++ b/Trigonometri.md @@ -6,6 +6,10 @@ - Ex: $$\begin{align}180^\circ=\pi\text{ rad}\\\frac{\pi}{3}\text{ rad}=30^\circ\\\frac{\pi}{4}\text{ rad}=45^\circ\\\frac{\pi}{3}\text{ rad}=60^\circ\\\frac{\pi}{2}\text{ rad}=90^\circ\\2\pi\text{ rad}=360^\circ\end{align}$$ - The right angled triangle - **Def**: *The trigonometric functions: *$$\begin{align}\sin\theta=\frac{\text{perpendicular}}{\text{hypotenuse}}\\\cos\theta=\frac{\text{base}}{\text{hypotenuse}}\\\tan\theta=\frac{\text{perpendicular}}{\text{base}}\end{align}$$ + - In addition to above, $\csc\theta=\frac{1}{\sin\theta},\sec\theta=\frac{1}{\cos\theta},\cot\theta=\frac{1}{\tan\theta}$ + - Pythagoras' formula: $p^2+b^2=h^2$ + which leads to the **trigonometric identity**: $\sin^2\theta+\cos^2\theta=1$ + and also $\tan^2\theta+1=\sec^2\theta$ - Dominains and ranges: - $D_{\sin}=\mathbb{R}\;\;R_{\sin}=[-1,1]$ - $D_{\cos}=\mathbb{R}\;\;R_{\cos}=[-1,1]$