Beispiel: Trigonometrische Identitäten

Funktionen > Trigonometrische, Logarithmus- und Exponentialfunktionen > Beispiel: Trigonometrische Identitäten

Beispiel: Trigonometrische Identitäten

Grundlegende Identitäten

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    <apply xmlns="http://schemas.mathsoft.com/math50">
      <equal />
      <apply>
        <plus />
        <apply>
          <pow />
          <apply>
            <id xml:space="preserve">sin</id>
            <id xml:space="preserve">x</id>
          </apply>
          <real>2</real>
        </apply>
        <apply>
          <pow />
          <apply>
            <id xml:space="preserve">cos</id>
            <id xml:space="preserve">x</id>
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          <real>2</real>
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      <real>1</real>
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Komplexe Identitäten

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        <apply>
          <minus />
          <apply>
            <pow />
            <id xml:space="preserve">e</id>
            <apply>
              <mult />
              <id xml:space="preserve">i</id>
              <id xml:space="preserve">z</id>
            </apply>
          </apply>
          <apply>
            <pow />
            <id xml:space="preserve">e</id>
            <apply>
              <mult />
              <apply>
                <neg />
                <id xml:space="preserve">i</id>
              </apply>
              <id xml:space="preserve">z</id>
            </apply>
          </apply>
        </apply>
        <apply>
          <mult />
          <real>2</real>
          <id xml:space="preserve">i</id>
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      </apply>
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      <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
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        <id xml:space="preserve">z</id>
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      <apply>
        <div />
        <apply>
          <plus />
          <apply>
            <pow />
            <id xml:space="preserve">e</id>
            <apply>
              <mult />
              <id xml:space="preserve">i</id>
              <id xml:space="preserve">z</id>
            </apply>
          </apply>
          <apply>
            <pow />
            <id xml:space="preserve">e</id>
            <apply>
              <mult />
              <apply>
                <neg />
                <id xml:space="preserve">i</id>
              </apply>
              <id xml:space="preserve">z</id>
            </apply>
          </apply>
        </apply>
        <real>2</real>
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          <id xml:space="preserve">i</id>
          <id xml:space="preserve">z</id>
        </apply>
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      <apply>
        <plus />
        <apply>
          <id xml:space="preserve">cos</id>
          <id xml:space="preserve">z</id>
        </apply>
        <apply>
          <mult />
          <id xml:space="preserve">i</id>
          <apply>
            <id xml:space="preserve">sin</id>
            <id xml:space="preserve">z</id>
          </apply>
        </apply>
      </apply>
    </apply>
    <resultFormat>
      <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
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          <id xml:space="preserve">x</id>
          <apply>
            <mult />
            <id xml:space="preserve">i</id>
            <id xml:space="preserve">y</id>
          </apply>
        </apply>
      </apply>
      <apply>
        <mult />
        <apply>
          <pow />
          <id xml:space="preserve">e</id>
          <id xml:space="preserve">x</id>
        </apply>
        <parens>
          <apply>
            <plus />
            <apply>
              <id xml:space="preserve">cos</id>
              <id xml:space="preserve">y</id>
            </apply>
            <apply>
              <mult />
              <id xml:space="preserve">i</id>
              <apply>
                <id xml:space="preserve">sin</id>
                <id xml:space="preserve">y</id>
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      <apply>
        <id xml:space="preserve">ln</id>
        <apply>
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          <id xml:space="preserve">x</id>
          <apply>
            <mult />
            <id xml:space="preserve">i</id>
            <id xml:space="preserve">y</id>
          </apply>
        </apply>
      </apply>
      <apply>
        <plus />
        <apply>
          <scale />
          <apply>
            <div />
            <real>1</real>
            <real>2</real>
          </apply>
          <apply>
            <id xml:space="preserve">ln</id>
            <apply>
              <plus />
              <apply>
                <pow />
                <id xml:space="preserve">x</id>
                <real>2</real>
              </apply>
              <apply>
                <pow />
                <id xml:space="preserve">y</id>
                <real>2</real>
              </apply>
            </apply>
          </apply>
        </apply>
        <apply>
          <mult />
          <id xml:space="preserve">i</id>
          <apply>
            <id xml:space="preserve">atan</id>
            <apply>
              <div />
              <id xml:space="preserve">y</id>
              <id xml:space="preserve">x</id>
            </apply>
          </apply>
        </apply>
      </apply>
    </apply>
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      <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
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Die Funktion ln0 ähnelt der Funktion ln, wird jedoch für null definiert.

Hyperbolische Funktionen und Exponentiale

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            <id xml:space="preserve">e</id>
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          <apply>
            <pow />
            <id xml:space="preserve">e</id>
            <apply>
              <neg />
              <id xml:space="preserve">x</id>
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          </apply>
        </apply>
        <real>2</real>
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            <pow />
            <id xml:space="preserve">e</id>
            <id xml:space="preserve">x</id>
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          <apply>
            <pow />
            <id xml:space="preserve">e</id>
            <apply>
              <neg />
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        <real>2</real>
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        <id xml:space="preserve">x</id>
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          <minus />
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            <pow />
            <id xml:space="preserve">e</id>
            <id xml:space="preserve">x</id>
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            <id xml:space="preserve">e</id>
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              <id xml:space="preserve">x</id>
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            <pow />
            <id xml:space="preserve">e</id>
            <id xml:space="preserve">x</id>
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            <pow />
            <id xml:space="preserve">e</id>
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Hyperbolische Funktionen und trigonometrische Beziehungen

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          <id xml:space="preserve">tan</id>
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Zugehörige Themen

Hyperbolische Funktionen

Trigonometrische Funktionen

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