From a09b5a99c0e4d4a47a9c49c80d0a136c4ed0f754 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Zacharias=20Zell=C3=A9n?= Date: Wed, 12 Nov 2025 17:01:15 +0100 Subject: [PATCH] vault backup: 2025-11-12 17:01:15 --- Trigonometri.md | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/Trigonometri.md b/Trigonometri.md index 67d393a..a75978f 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: - $D_{\sin}=\mathbb{R}\;\;R_{\sin}=[-1,1]$ - $D_{\cos}=\mathbb{R}\;\;R_{\cos}=[-1,1]$