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Diffstat (limited to 'html/topic/mathematics.html')
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1 files changed, 21 insertions, 20 deletions
diff --git a/html/topic/mathematics.html b/html/topic/mathematics.html index 91c2557..f3abbe0 100644 --- a/html/topic/mathematics.html +++ b/html/topic/mathematics.html @@ -108,62 +108,63 @@ <p class="math">\(hypotenuse=modliggende_{\gamma}=c\)</p> </div> <div class="group"> + <p>I en retvinklet trekant:</p> <p class="math">\(sin(\theta)=\frac {modliggende_{\theta}}{hypotenuse_{\theta}}\)</p> <p class="math">\(cos(\theta)=\frac {hosliggende_{\theta}}{hypotenuse_{\theta}}\)</p> <p class="math">\(tan(\theta)=\frac {modliggende_{\theta}}{hosliggende_{\theta}}\)</p> - <p class="math">\(cot(\theta)=\frac {hosliggende_{\theta}}{modliggende_{\theta}}\)</p> - <p class="math">\(csc(\theta)=\frac {hypotenuse_{\theta}}{modliggende_{\theta}}\)</p> - <p class="math">\(sec(\theta)=\frac {hypotenuse_{\theta}}{hosliggende_{\theta}}\)</p> + <p class="math">\(csc(\theta)=\frac 1{sin(\theta)}=\frac {hypotenuse_{\theta}}{modliggende_{\theta}}\)</p> + <p class="math">\(sec(\theta)=\frac 1{cos(\theta)}=\frac {hypotenuse_{\theta}}{hosliggende_{\theta}}\)</p> + <p class="math">\(cot(\theta)=\frac 1{tan(\theta)}=\frac {hosliggende_{\theta}}{modliggende_{\theta}}\)</p> </div> <div class="group"> + <p>I en retvinklet trekant:</p> <p class="math">\(sin^{-1}(\frac {modliggende_{\theta}}{hypotenuse_{\theta}})=\theta\)</p> <p class="math">\(cos^{-1}(\frac {hosliggende_{\theta}}{hypotenuse_{\theta}})=\theta\)</p> <p class="math">\(tan^{-1}(\frac {modliggende_{\theta}}{hosliggende_{\theta}})=\theta\)</p> - <p class="math">\(cot^{-1}(\frac {hosliggende_{\theta}}{modliggende_{\theta}})=\theta\)</p> <p class="math">\(csc^{-1}(\frac {hypotenuse_{\theta}}{modliggende_{\theta}})=\theta\)</p> <p class="math">\(sec^{-1}(\frac {hypotenuse_{\theta}}{hosliggende_{\theta}})=\theta\)</p> + <p class="math">\(cot^{-1}(\frac {hosliggende_{\theta}}{modliggende_{\theta}})=\theta\)</p> </div> <div class="group"> <p>Forkortelser:</p> <p class="math">\(sin=sinus\)</p> <p class="math">\(cos=cosinus\)</p> <p class="math">\(tan=tangens\)</p> - <p class="math">\(cot=cotangens\)</p> <p class="math">\(csc=cosekant\)</p> <p class="math">\(sec=sekant\)</p> + <p class="math">\(cot=cotangens\)</p> <p class="math">\(arcsin=sin^{-1}\)</p> <p class="math">\(arccos=cos^{-1}\)</p> <p class="math">\(arctan=tan^{-1}\)</p> - <p class="math">\(arccot=cot^{-1}\)</p> - <p class="math">\(arcsec=sec^{-1}\)</p> <p class="math">\(arccsc=csc^{-1}\)</p> + <p class="math">\(arcsec=sec^{-1}\)</p> + <p class="math">\(arccot=cot^{-1}\)</p> </div> <div class="group"> <p class="math">\(deg(rad)=\frac {rad \cdot 180}{\pi}\)</p> <p class="math">\(rad(deg)=\frac {deg \cdot \pi}{180}\)</p> </div> <div class="group"> - <p class="math">\(\Theta(n)=(n-2)\pi\)</p> + <p class="math">\(\Theta(n)=\pi(n-2)\)</p> <p class="note">hvori <span class="math">\({\Theta}(n)\)</span> er vinkelsummen af <span class="emphasis">n</span>-gonen.</p> - <p class="math">\(\Theta(3)=(3-2)\pi=\pi\)</p> + <p class="math">\(\Theta(3)=\pi\)</p> </div> <div class="group"> - <p class="math">\(\alpha=sin^{-1}(\frac ac)=cos^{-1}(\frac bc)=tan^{-1}(\frac ab)=\Theta(3)-\beta-\gamma\)</p> - <p class="math">\(\beta=sin^{-1}(\frac bc)=cos^{-1}(\frac ac)=tan^{-1}(\frac ba)=\Theta(3)-\alpha-\gamma\)</p> - <p class="math">\(\gamma=\Theta(3)-\alpha-\beta\)</p> + <p class="math">\(\alpha=\pi-\beta-\gamma\)</p> + <p class="math">\(\beta=\pi-\alpha-\gamma\)</p> + <p class="math">\(\gamma=\pi-\alpha-\beta\)</p> <p>I en retvinklet trekant:</p> + <p class="math">\(\alpha=sin^{-1}(\frac ac)=cos^{-1}(\frac bc)=tan^{-1}(\frac ab)\)</p> + <p class="math">\(\beta=sin^{-1}(\frac bc)=cos^{-1}(\frac ac)=tan^{-1}(\frac ba)\)</p> <p class="math">\(\gamma=\frac {\pi}2\)</p> <p>I en regulær trekant:</p> <p class="math">\(\alpha=\beta=\gamma=\frac {\pi}3\)</p> </div> <div class="group"> - <p class="math">\(a=c \cdot sin(\alpha)=c \cdot cos(\beta)=b \cdot tan(\alpha)=b \cdot cot(\beta)\)</p> - <p class="math">\(b=c \cdot sin(\beta)=c \cdot cos(\alpha)=a \cdot tan(\beta)=a \cdot cot(\alpha)\)</p> - <p class="math">\(c=a \cdot csc(\alpha)=b \cdot csc(\beta)=a \cdot sec(\beta)=b \cdot sec(\alpha)\)</p> <p>I en retvinklet trekant:</p> - <p class="math">\(a=\sqrt[2] {c^2-b^2}\)</p> - <p class="math">\(b=\sqrt[2] {c^2-a^2}\)</p> - <p class="math">\(c=\sqrt[2] {a^2+b^2}\)</p> + <p class="math">\(a=c \cdot sin(\alpha)=c \cdot cos(\beta)=b \cdot tan(\alpha)=b \cdot cot(\beta)=\sqrt[2] {c^2-b^2}\)</p> + <p class="math">\(b=c \cdot sin(\beta)=c \cdot cos(\alpha)=a \cdot tan(\beta)=a \cdot cot(\alpha)=\sqrt[2] {c^2-a^2}\)</p> + <p class="math">\(c=a \cdot csc(\alpha)=b \cdot csc(\beta)=a \cdot sec(\beta)=b \cdot sec(\alpha)=\sqrt[2] {a^2+b^2}\)</p> <p>I en retvinklet trekant, hvori kateterne har samme længde:</p> <p class="math">\(a=b=\sqrt[2] {\frac {c^2}2}\)</p> <p>I en regulær trekant:</p> @@ -221,7 +222,7 @@ </tr> <tr> <td><sub>den </sub>gyldne ratio</td> - <td class="math">\(\phi\)</td> + <td class="math">\(\varphi\)</td> </tr> </tbody> </table> @@ -232,7 +233,7 @@ <p class="math">\(i=\sqrt[2] {-1}\)</p> <p class="math">\(\pi \approx \frac {3\ 141\ 592\ 654}{10^9}\)</p> <p class="math">\(\tau=2\pi \approx \frac {6\ 283\ 185\ 307}{10^9}\)</p> - <p class="math">\(\phi=\frac {1+\sqrt[2] 5}2 \approx \frac {1\ 618\ 033\ 989}{10^9}\)</p> + <p class="math">\(\varphi=\frac {1+\sqrt[2] 5}2 \approx \frac {1\ 618\ 033\ 989}{10^9}\)</p> </div> </div> </div> |