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<!DOCTYPE html>
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<p class="pagePath"><a href="/html/encyclopedia.html">encyclopedia</a> / <a href="/html/encyclopedia.html#mathematics">mathematics</a> / <a href="/html/encyclopedia/mathematics/trigonometry.html">conjugation</a></p>
<p class="pageTitle">Leksikon</p>
<div class="section">
<p class="math">\(modliggende_{\angle A} = hosliggende_{\angle B} = a\)</p>
<p class="math">\(hosliggende_{\angle A} = modliggende_{\angle B} = b\)</p>
<p class="math">\(hypotenuse = modliggende_{\angle C} = c\)</p>
<br />
<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>
<br />
<p class="math">\(sin(\theta) = \frac{modliggende}{hypotenuse}\)</p>
<p class="math">\(cos(\theta) = \frac{hosliggende}{hypotenuse}\)</p>
<p class="math">\(tan(\theta) = \frac{modliggende}{hosliggende}\)</p>
<p class="math">\(cot(\theta) = \frac{hosliggende}{modliggende}\)</p>
<p class="math">\(csc(\theta) = \frac{hypotenuse}{modliggende}\)</p>
<p class="math">\(sec(\theta) = \frac{hypotenuse}{hosliggende}\)</p>
<br />
<p class="math">\(x = f ^ {-1} (f(x))\)</p>
<p class="math">\(sin ^ {-1} (\frac{modliggende}{hypotenuse}) = \theta\)</p>
<p class="math">\(cos ^ {-1} (\frac{hosliggende}{hypotenuse}) = \theta\)</p>
<p class="math">\(tan ^ {-1} (\frac{modliggende}{hosliggende}) = \theta\)</p>
<p class="math">\(cot ^ {-1} (\frac{hosliggende}{modliggende}) = \theta\)</p>
<p class="math">\(csc ^ {-1} (\frac{hypotenuse}{modliggende}) = \theta\)</p>
<p class="math">\(sec ^ {-1} (\frac{hypotenuse}{hosliggende}) = \theta\)</p>
<br />
<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>
<br />
<p class="math">\(deg(rad) = \frac{x}{\frac{\pi}{180}}\)</p>
<p class="math">\(rad(deg) = \frac{x}{\frac{180}{\pi}}\)</p>
<br />
<p class="math">\(vinkelsum(x) = \pi(x - 2)\)</p>
<p class="math">\(vinkelsum(3) = \pi(3 - 2) = \pi(1) = \pi\)</p>
<br />
<p class="math">\(\angle A = sin ^ {-1} (\frac{a}{c}) = cos ^ {-1} (\frac{b}{c}) = tan ^ {-1} (\frac{a}{b}) = vinkelsum(3) - \angle B - \angle C\)</p>
<p class="math">\(\angle B = sin ^ {-1} (\frac{b}{c}) = cos ^ {-1} (\frac{a}{c}) = tan ^ {-1} (\frac{b}{a}) = vinkelsum(3) - \angle A - \angle C\)</p>
<p class="math">\(\angle C = vinkelsum(3) - \angle A - \angle B\)</p>
<p>I en regulær trekant:</p>
<p class="math">\(\angle A = \angle B = \angle C\)</p>
<p>I en retvinklet trekant:</p>
<p class="math">\(\angle C = \frac{\pi}{2}\)</p>
<br />
<p class="math">\(a = c ⋅ sin(\angle A) = c ⋅ cos(\angle B) = b ⋅ tan(\angle A) = b ⋅ cot(\angle B)\)</p>
<p class="math">\(b = c ⋅ sin(\angle B) = c ⋅ cos(\angle A) = a ⋅ tan(\angle B) = a ⋅ cot(\angle A)\)</p>
<p class="math">\(c = a ⋅ csc(\angle A) = b ⋅ csc(\angle B) = a ⋅ sec(\angle B) = b ⋅ sec(\angle A)\)</p>
<p>I en regulær trekant:</p>
<p class="math">\(a = b = c\)</p>
<p>I en retvinklet trekant:</p>
<p class="math">\(c = \sqrt[2]{a ^ 2 + b ^ 2}\)</p>
<p>I en retvinklet trekant, hvori kateterne har samme længde:</p>
<p class="math">\(a = b = \sqrt[2]{\frac{c ^ 2}{2}}\)</p>
<br />
<p class="math">\(O = a + b + c\)</p>
<p class="math">\(A = \frac{b ⋅ h}{2}\)</p>
<p>Mellem to ligedannet trekanter:</p>
<p class="math">\(\angle A_{1} = \angle A_{0}\)</p>
<p class="math">\(\angle B_{1} = \angle B_{0}\)</p>
<p class="math">\(\angle C_{1} = \angle C_{0}\)</p>
<p class="math">\(k = \frac{a_{1}}{a_{0}} = \frac{b_{1}}{b_{0}} = \frac{c_{1}}{c_{0}}\)</p>
<p class="math">\(a_{1} = a_{0} k\)</p>
<p class="math">\(b_{1} = b_{0} k\)</p>
<p class="math">\(c_{1} = c_{0} k\)</p>
<p class="math">\(O_{1} = O_{0} k\)</p>
<p class="math">\(A_{1} = A_{0} k ^ 2\)</p>
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