예제: 삼각 항등식

함수 > 삼각, 로그 및 지수 > 예제: 삼각 항등식

예제: 삼각 항등식

기본 항등식

<region id="ID0EOSODB" top="211.20000000000005" left="19.200000000000003" height="34" width="150.05666666666664" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="50">
    <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>
          </apply>
          <real>2</real>
        </apply>
      </apply>
      <real>1</real>
    </apply>
    <resultFormat>
      <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

복소수 항등식

<region id="ID0EPUODB" top="441.60000000000008" left="19.200000000000003" height="49.352000000000004" width="137.53000000000003" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="58">
    <apply xmlns="http://schemas.mathsoft.com/math50">
      <equal />
      <apply>
        <id xml:space="preserve">sin</id>
        <id xml:space="preserve">z</id>
      </apply>
      <apply>
        <div />
        <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>
        </apply>
      </apply>
    </apply>
    <resultFormat>
      <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

<region id="ID0E4UODB" top="480.00000000000006" left="19.200000000000003" height="49.352000000000004" width="137.83666666666667" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="60">
    <apply xmlns="http://schemas.mathsoft.com/math50">
      <equal />
      <apply>
        <id xml:space="preserve">cos</id>
        <id xml:space="preserve">z</id>
      </apply>
      <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>
      </apply>
    </apply>
    <resultFormat>
      <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

<region id="ID0ELVODB" top="537.60000000000014" left="19.200000000000003" height="27.752000000000002" width="158.92000000000002" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="62">
    <apply xmlns="http://schemas.mathsoft.com/math50">
      <equal />
      <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>
        <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" />
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

<region id="ID0EZVODB" top="576.00000000000011" left="19.200000000000003" height="27.752000000000002" width="215.66666666666669" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="64">
    <apply xmlns="http://schemas.mathsoft.com/math50">
      <equal />
      <apply>
        <pow />
        <id xml:space="preserve">e</id>
        <apply>
          <plus />
          <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>
              </apply>
            </apply>
          </apply>
        </parens>
      </apply>
    </apply>
    <resultFormat>
      <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

<region id="ID0EHWODB" top="633.60000000000014" left="19.200000000000003" height="47.2" width="279.2166666666667" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="66">
    <apply xmlns="http://schemas.mathsoft.com/math50">
      <equal />
      <apply>
        <id xml:space="preserve">ln</id>
        <apply>
          <plus />
          <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>
    <resultFormat>
      <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

ln0 함수는 ln과 유사하지만 0에서 정의되어 있습니다.

쌍곡선 함수와 지수

<region id="ID0EYZODB" top="844.80000000000018" left="38.400000000000006" height="49.352000000000004" width="131.08333333333334" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="72">
    <apply xmlns="http://schemas.mathsoft.com/math50">
      <equal />
      <apply>
        <id xml:space="preserve">sinh</id>
        <id xml:space="preserve">x</id>
      </apply>
      <apply>
        <div />
        <apply>
          <minus />
          <apply>
            <pow />
            <id xml:space="preserve">e</id>
            <id xml:space="preserve">x</id>
          </apply>
          <apply>
            <pow />
            <id xml:space="preserve">e</id>
            <apply>
              <neg />
              <id xml:space="preserve">x</id>
            </apply>
          </apply>
        </apply>
        <real>2</real>
      </apply>
    </apply>
    <resultFormat>
      <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

<region id="ID0EG1ODB" top="883.20000000000016" left="38.400000000000006" height="49.352000000000004" width="131.39000000000002" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="74">
    <apply xmlns="http://schemas.mathsoft.com/math50">
      <equal />
      <apply>
        <id xml:space="preserve">cosh</id>
        <id xml:space="preserve">x</id>
      </apply>
      <apply>
        <div />
        <apply>
          <plus />
          <apply>
            <pow />
            <id xml:space="preserve">e</id>
            <id xml:space="preserve">x</id>
          </apply>
          <apply>
            <pow />
            <id xml:space="preserve">e</id>
            <apply>
              <neg />
              <id xml:space="preserve">x</id>
            </apply>
          </apply>
        </apply>
        <real>2</real>
      </apply>
    </apply>
    <resultFormat>
      <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

<region id="ID0EU1ODB" top="940.80000000000018" left="38.400000000000006" height="51.504000000000005" width="133.66666666666666" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="76">
    <apply xmlns="http://schemas.mathsoft.com/math50">
      <equal />
      <apply>
        <id xml:space="preserve">tanh</id>
        <id xml:space="preserve">x</id>
      </apply>
      <apply>
        <div />
        <apply>
          <minus />
          <apply>
            <pow />
            <id xml:space="preserve">e</id>
            <id xml:space="preserve">x</id>
          </apply>
          <apply>
            <pow />
            <id xml:space="preserve">e</id>
            <apply>
              <neg />
              <id xml:space="preserve">x</id>
            </apply>
          </apply>
        </apply>
        <apply>
          <plus />
          <apply>
            <pow />
            <id xml:space="preserve">e</id>
            <id xml:space="preserve">x</id>
          </apply>
          <apply>
            <pow />
            <id xml:space="preserve">e</id>
            <apply>
              <neg />
              <id xml:space="preserve">x</id>
            </apply>
          </apply>
        </apply>
      </apply>
    </apply>
    <resultFormat>
      <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

쌍곡선 함수와 삼각 관계

<region id="ID0ER4ODB" top="1286.4" left="19.200000000000003" height="25.6" width="159.23666666666668" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="88">
    <apply xmlns="http://schemas.mathsoft.com/math50">
      <equal />
      <apply>
        <id xml:space="preserve">tanh</id>
        <id xml:space="preserve">z</id>
      </apply>
      <apply>
        <mult />
        <apply>
          <neg />
          <id xml:space="preserve">i</id>
        </apply>
        <apply>
          <id xml:space="preserve">tan</id>
          <apply>
            <mult />
            <id xml:space="preserve">i</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" />
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

관련 항목

쌍곡선 함수

삼각 함수

도움이 되셨나요?