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From: =?UTF-8?q?Anton=20Luka=20=C5=A0ijanec?= <anton@sijanec.eu>
Date: Wed, 2 Feb 2022 22:39:19 +0100
Subject: =?UTF-8?q?fizika=20vaja=202=20in=20=C5=A1e=20kaj?=
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---
 mat/trigonometrija.tex | 45 +++++++++++++++++++++++++++++++++++++--------
 1 file changed, 37 insertions(+), 8 deletions(-)

(limited to 'mat/trigonometrija.tex')

diff --git a/mat/trigonometrija.tex b/mat/trigonometrija.tex
index cb65720..c9cfff5 100644
--- a/mat/trigonometrija.tex
+++ b/mat/trigonometrija.tex
@@ -11,6 +11,7 @@
 \usepackage{tkz-euclide}
 \usepackage{amssymb}
 \usepackage{multicol}
+\usepackage{amsmath}
 % \sisetup{output-decimal-marker = {,}, quotient-mode=fraction, per-mode=fraction}	% frac način
 % \sisetup{output-decimal-marker = {,}, quotient-mode=fraction, per-mode=symbol}	% poševnica način
 \sisetup{output-decimal-marker = {,}, quotient-mode=fraction}				% na -1 način
@@ -35,18 +36,21 @@
 % Spisek izbranih trigonometričnih izrekov bom kot pripomoček imel na drugem testu pri matematiki v tretjem letniku.
 % \end{abstract}
 % \tableofcontents
+\section{Drugi test}
 \begin{multicols}{2}
-	\begin{tabular}{|c|c|c|c|c|}
+	\begin{tabular}{|c|c|c|c|c|c|}
 		\hline
-		$\measuredangle$	& $\sin$		& $\cos$		& $\tan$		& $\cot$		\\
+		$\measuredangle$	& Rad		& $\sin$		& $\cos$		& $\tan$		& $\cot$		\\
 		\hline
-		$\ang{30}$		& 0			& 1			& 0			& ne obstaja		\\
+		$\ang{0}$		& 0		& 0			& 1			& 0			& ne obstaja		\\
 		\hline
-		$\ang{45}$		& $\frac{1}{2}$	& $\frac{\sqrt{3}}{2}$	& $\frac{\sqrt{3}}{2}$	& $\sqrt{3}$		\\
+		$\ang{30}$		&$\frac{\pi}{6}$& $\frac{1}{2}$		& $\frac{\sqrt{3}}{2}$	& $\frac{\sqrt{3}}{2}$	& $\sqrt{3}$		\\
 		\hline
-		$\ang{60}$		& $\frac{\sqrt{3}}{2}$	& $\frac{1}{2}$		& $\sqrt{3}$		& $\frac{\sqrt{3}}{3}$	\\
+		$\ang{45}$		& $\frac{\pi}{4}$& $\frac{\sqrt{2}}{2}$	& $\frac{\sqrt{2}}{2}$	& 1			& 1			\\
 		\hline
-		$\ang{90}$		& 1			& 0			& ne obstaja		& 0			\\
+		$\ang{60}$		& $\frac{\pi}{3}$& $\frac{\sqrt{3}}{2}$	& $\frac{1}{2}$		& $\sqrt{3}$		& $\frac{\sqrt{3}}{3}$	\\
+		\hline
+		$\ang{90}$		& $\frac{\pi}{2}$& 1			& 0			& ne obstaja		& 0			\\
 		\hline
 	\end{tabular}
 	$$\sin^2\alpha+\cos^2\alpha=1$$
@@ -80,12 +84,37 @@
 	$$\sin\alpha\pm\sin\beta=2\sin\left(\frac{\alpha\pm\beta}{2}\right)\cos\left(\frac{\alpha\mp\beta}{2}\right)$$
 	$$\cos\alpha+\cos\beta=2\cos\left(\frac{\alpha+\beta}{2}\right)\cos\left(\frac{\alpha-\beta}{2}\right)$$
 	$$\cos\alpha-\cos\beta=-2\sin\left(\frac{\alpha+\beta}{2}\right)\sin\left(\frac{\alpha-\beta}{2}\right)$$
-	$$\tan\alpha+\tan\beta=\frac{\sin\left(\alpha+\beta\right)}{\cos\alpha\cos\beta}$$
+	$$\tan\alpha\pm\tan\beta=\frac{\sin\left(\alpha\pm\beta\right)}{\cos\alpha\cos\beta}$$
 	$$\sin\alpha\cos\alpha=\frac{1}{2}\sin2\alpha$$
 	$$2\cos^2\frac{\alpha}{2}=1+\cos\alpha$$
 	$$2\sin^2\frac{\alpha}{2}=1-\cos\alpha$$
 	$$\tan^2\frac{x}{2}=\frac{1-\cos\alpha}{1+\cos\alpha}$$
-	$$\cos\frac{\alpha}{2}=\pm\sqrt{\frac{1+\cos\alpha}{2}} \text{ in tako dalje}$$
+\end{multicols}
+\section{Tretji test}
+\begin{multicols}{2}
+	$$s=\frac{a+b+c}{2} \wedge S=\sqrt{s(s-a)(s-b)(s-c)}$$
+	$$S_\text{trikotnika v izseku}=\frac{r^2\sin\alpha}{2}$$
+	$$\frac{a}{\sin\alpha}=\frac{b}{\sin\beta}=\frac{c}{\sin\gamma}=2R$$
+	$$a^2=b^2+c^2-2bc\cos\alpha$$
+	$$S_\text{paralelograma}=av_a=ab\sin\alpha=\frac{ef}{2}\sin\omega$$
+	$$S_\text{romba}=av=a^2\sin\alpha=\frac{ef}{2}$$
+	$$S_\text{trapeza}=\frac{v(a+c)}{2}$$
+	$$S_\text{deltoida}=\frac{ef}{2}$$
+	$$S_\text{trikotnika}=\frac{ab\sin\gamma}{2}=\frac{av_a}{2}$$
+	$$S_\text{enakostraničnega}=\frac{a^2\sqrt{3}}{4}$$
+	$$\arcsin x+\arccos x=\frac{\pi}{2}$$
+	$$S_\text{trikotnika}=\frac{abc}{4R}=2R^2\sin\alpha\sin\beta\sin\gamma=rs\text{, kjer je } s=\frac{a+b+c}{2}$$
+	$$Diagonal_\text{pravilnega mnogokotnika}=\frac{n(n-3)}{2}$$
+	$$\alpha_\text{pravilnega mnogokotnika}=\frac{n-2}{n}\ang{180}$$
+	$$S_\text{pravilnega mnogokotnika}=\frac{n}{2}R^2\sin\frac{\ang{360}}{n}=
+		na^2\tan\frac{\alpha}{2}\frac{1}{2}=\frac{na^2}{4\tan\frac{\ang{180}}{n}}$$
+	$$\alpha_\text{ene premice}=\arctan k_p$$
+	$$\alpha_\text{med dvema premicama}=\arctan\lvert\frac{k_q-k_p}{1+k_p-k_q}\rvert$$
+	$$D_\text{arcsin}=D_\text{arccos}=[-1; 1] \wedge V_\text{arcsin}=[\ang{-90}; \ang{90}] \wedge V_\text{arccos}=[\ang{0}; \ang{180}]$$
+	$$D_\text{arctan}=D_\text{arccot}=\mathbb{R} \wedge V_\text{arctan}=(\ang{-90}; \ang{90}) \wedge V_\text{arccot}=(\ang{0}; \ang{180})$$
+	$$soda(x)=-soda(x) \wedge liha(-x)=-liha(x)$$
+	$$f(x)\neq-f(x)\nLeftrightarrow f(-x)=-f(x) \text{ in obratno}$$
+	$$f(x)=-f(x) \wedge f(-x)=-f(x) \Leftrightarrow f(x)=0$$
 \end{multicols}
 \section{Zaključek}
 \hologo{LaTeX} izvorna koda dokumenta je objavljena na \url{https://git.sijanec.eu/sijanec/sola-gimb-3}. Za izdelavo dokumenta je potreben \texttt{TeXLive 2020}.
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cgit v1.2.3

