@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

psr:-B7HW69DB-5
  skos:altLabel "sine rule"@en, "sine formula"@en, "sine law"@en, "formule des sinus"@fr ;
  skos:related psr:-RX61SX55-G ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Loi_des_sinus>, <https://en.wikipedia.org/wiki/Law_of_sines> ;
  skos:broader psr:-LN44RXKJ-J, psr:-JL9Z4260-Z ;
  skos:prefLabel "law of sines"@en, "loi des sinus"@fr ;
  a skos:Concept ;
  skos:inScheme psr: ;
  skos:definition """En trigonométrie, la loi des sinus est une relation de proportionnalité entre les longueurs des côtés d'un triangle et les sinus des angles respectivement opposés. Elle permet, connaissant deux angles et un côté, de calculer la longueur des autres côtés. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Loi_des_sinus">https://fr.wikipedia.org/wiki/Loi_des_sinus</a>)"""@fr, """In trigonometry, the <b>law of sines</b>, <b>sine law</b>, <b>sine formula</b>, or <b>sine rule</b> is an equation relating the lengths of the sides of any triangle to the sines of its angles. According to the law,
<br/><div class="mwe-math-element"><div class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle {\\rac {a}{\\\\sin {\\\\alpha }}}\\\\,=\\\\,{\\rac {b}{\\\\sin {\\eta }}}\\\\,=\\\\,{\\rac {c}{\\\\sin {\\\\gamma }}}\\\\,=\\\\,2R,}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <mi>a</mi>
<br/>            <mrow>
<br/>              <mi>sin</mi>
<br/>              <mo>⁡<!-- ⁡ --></mo>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mi>α<!-- α --></mi>
<br/>              </mrow>
<br/>            </mrow>
<br/>          </mfrac>
<br/>        </mrow>
<br/>        <mspace width="thinmathspace"></mspace>
<br/>        <mo>=</mo>
<br/>        <mspace width="thinmathspace"></mspace>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <mi>b</mi>
<br/>            <mrow>
<br/>              <mi>sin</mi>
<br/>              <mo>⁡<!-- ⁡ --></mo>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mi>β<!-- β --></mi>
<br/>              </mrow>
<br/>            </mrow>
<br/>          </mfrac>
<br/>        </mrow>
<br/>        <mspace width="thinmathspace"></mspace>
<br/>        <mo>=</mo>
<br/>        <mspace width="thinmathspace"></mspace>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <mi>c</mi>
<br/>            <mrow>
<br/>              <mi>sin</mi>
<br/>              <mo>⁡<!-- ⁡ --></mo>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mi>γ<!-- γ --></mi>
<br/>              </mrow>
<br/>            </mrow>
<br/>          </mfrac>
<br/>        </mrow>
<br/>        <mspace width="thinmathspace"></mspace>
<br/>        <mo>=</mo>
<br/>        <mspace width="thinmathspace"></mspace>
<br/>        <mn>2</mn>
<br/>        <mi>R</mi>
<br/>        <mo>,</mo>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle {\\rac {a}{\\\\sin {\\\\alpha }}}\\\\,=\\\\,{\\rac {b}{\\\\sin {\\eta }}}\\\\,=\\\\,{\\rac {c}{\\\\sin {\\\\gamma }}}\\\\,=\\\\,2R,}</annotation>
<br/>  </semantics>
<br/></math></div><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/190a39f2f01a92ea4ef8bb57885b9a962a986943" class="mwe-math-fallback-image-display" aria-hidden="true" style="vertical-align: -2.338ex; width:31.51ex; height:5.843ex;" alt="{\\\\displaystyle {\\rac {a}{\\\\sin {\\\\alpha }}}\\\\,=\\\\,{\\rac {b}{\\\\sin {\\eta }}}\\\\,=\\\\,{\\rac {c}{\\\\sin {\\\\gamma }}}\\\\,=\\\\,2R,}"></div>
<br/>where <span class="texhtml"><i>a</i>, <i>b</i></span>, and <span class="texhtml"><i>c</i></span> are the lengths of the sides of a triangle, and <span class="texhtml"><i>α</i>, <i>β</i></span>, and <span class="texhtml"><i>γ</i></span> are the opposite angles (see figure 2), while <span class="texhtml"><i>R</i></span> is the radius of the triangle's circumcircle. When the last part of the equation is not used, the law is sometimes stated using the reciprocals;
<br/><div class="mwe-math-element"><div class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle {\\rac {\\\\sin {\\\\alpha }}{a}}\\\\,=\\\\,{\\rac {\\\\sin {\\eta }}{b}}\\\\,=\\\\,{\\rac {\\\\sin {\\\\gamma }}{c}}.}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <mrow>
<br/>              <mi>sin</mi>
<br/>              <mo>⁡<!-- ⁡ --></mo>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mi>α<!-- α --></mi>
<br/>              </mrow>
<br/>            </mrow>
<br/>            <mi>a</mi>
<br/>          </mfrac>
<br/>        </mrow>
<br/>        <mspace width="thinmathspace"></mspace>
<br/>        <mo>=</mo>
<br/>        <mspace width="thinmathspace"></mspace>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <mrow>
<br/>              <mi>sin</mi>
<br/>              <mo>⁡<!-- ⁡ --></mo>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mi>β<!-- β --></mi>
<br/>              </mrow>
<br/>            </mrow>
<br/>            <mi>b</mi>
<br/>          </mfrac>
<br/>        </mrow>
<br/>        <mspace width="thinmathspace"></mspace>
<br/>        <mo>=</mo>
<br/>        <mspace width="thinmathspace"></mspace>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <mrow>
<br/>              <mi>sin</mi>
<br/>              <mo>⁡<!-- ⁡ --></mo>
<br/>              <mrow class="MJX-TeXAtom-ORD">
<br/>                <mi>γ<!-- γ --></mi>
<br/>              </mrow>
<br/>            </mrow>
<br/>            <mi>c</mi>
<br/>          </mfrac>
<br/>        </mrow>
<br/>        <mo>.</mo>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle {\\rac {\\\\sin {\\\\alpha }}{a}}\\\\,=\\\\,{\\rac {\\\\sin {\\eta }}{b}}\\\\,=\\\\,{\\rac {\\\\sin {\\\\gamma }}{c}}.}</annotation>
<br/>  </semantics>
<br/></math></div><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/21c772e7d03ba0626a817e423924bf359075a713" class="mwe-math-fallback-image-display" aria-hidden="true" style="vertical-align: -2.005ex; width:24.711ex; height:5.509ex;" alt="{\\\\displaystyle {\\rac {\\\\sin {\\\\alpha }}{a}}\\\\,=\\\\,{\\rac {\\\\sin {\\eta }}{b}}\\\\,=\\\\,{\\rac {\\\\sin {\\\\gamma }}{c}}.}"></div> 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Law_of_sines">https://en.wikipedia.org/wiki/Law_of_sines</a>)"""@en ;
  dc:modified "2023-08-10"^^xsd:date ;
  dc:created "2023-08-10"^^xsd:date .

psr:-JL9Z4260-Z
  skos:prefLabel "trigonométrie"@fr, "trigonometry"@en ;
  a skos:Concept ;
  skos:narrower psr:-B7HW69DB-5 .

psr: a skos:ConceptScheme .
psr:-RX61SX55-G
  skos:prefLabel "triangle"@fr, "triangle"@en ;
  a skos:Concept ;
  skos:related psr:-B7HW69DB-5 .

psr:-LN44RXKJ-J
  skos:prefLabel "trigonométrie sphérique"@fr, "spherical trigonometry"@en ;
  a skos:Concept ;
  skos:narrower psr:-B7HW69DB-5 .