Jump to navigation Jump to search

General

Display information for equation id:math.218594.0 on revision:218594

* Page found: Antiprism (eq math.218594.0)

(force rerendering)

Cannot find the equation data in the database. Fetching from revision text.

Occurrences on the following pages:

Hash: 660719bb966820893a1a8651c00d8d95

TeX (original user input):

\left( \cos\frac{k\pi}{n}, \sin\frac{k\pi}{n}, (-1)^k h \right)

TeX (checked):

\left(\cos {\frac {k\pi }{n}},\sin {\frac {k\pi }{n}},(-1)^{k}h\right)

LaTeXML (experimental; uses MathML) rendering

MathML (5.183 KB / 988 B) :

( cos k π n , sin k π n , ( - 1 ) k h ) 𝑘 𝜋 𝑛 𝑘 𝜋 𝑛 superscript 1 𝑘 {\displaystyle\left(\cos{\frac{k\pi}{n}},\sin{\frac{k\pi}{n}},(-1)^{k}h\right)}
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle\left(\cos{\frac{k\pi}{n}},\sin{\frac{k\pi}{n}},(-1)^{k}h\right)}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.15" xref="p1.1.m1.1.15.1.cmml">
      <mo id="p1.1.m1.1.1" xref="p1.1.m1.1.15.1.cmml">(</mo>
      <mrow id="p1.1.m1.1.15.2" xref="p1.1.m1.1.15.2.cmml">
        <mi id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">cos</mi>
        <mo id="p1.1.m1.1.15.2a" xref="p1.1.m1.1.15.2.cmml"></mo>
        <mstyle displaystyle="true" id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">
          <mfrac id="p1.1.m1.1.3a" xref="p1.1.m1.1.3.cmml">
            <mrow id="p1.1.m1.1.3.2" xref="p1.1.m1.1.3.2.cmml">
              <mi id="p1.1.m1.1.3.2.1" xref="p1.1.m1.1.3.2.1.cmml">k</mi>
              <mo id="p1.1.m1.1.3.2.3" xref="p1.1.m1.1.3.2.3.cmml"></mo>
              <mi id="p1.1.m1.1.3.2.2" xref="p1.1.m1.1.3.2.2.cmml">π</mi>
            </mrow>
            <mi id="p1.1.m1.1.3.3" xref="p1.1.m1.1.3.3.cmml">n</mi>
          </mfrac>
        </mstyle>
      </mrow>
      <mo id="p1.1.m1.1.4" xref="p1.1.m1.1.15.1.cmml">,</mo>
      <mrow id="p1.1.m1.1.15.3" xref="p1.1.m1.1.15.3.cmml">
        <mi id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">sin</mi>
        <mo id="p1.1.m1.1.15.3a" xref="p1.1.m1.1.15.3.cmml"></mo>
        <mstyle displaystyle="true" id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">
          <mfrac id="p1.1.m1.1.6a" xref="p1.1.m1.1.6.cmml">
            <mrow id="p1.1.m1.1.6.2" xref="p1.1.m1.1.6.2.cmml">
              <mi id="p1.1.m1.1.6.2.1" xref="p1.1.m1.1.6.2.1.cmml">k</mi>
              <mo id="p1.1.m1.1.6.2.3" xref="p1.1.m1.1.6.2.3.cmml"></mo>
              <mi id="p1.1.m1.1.6.2.2" xref="p1.1.m1.1.6.2.2.cmml">π</mi>
            </mrow>
            <mi id="p1.1.m1.1.6.3" xref="p1.1.m1.1.6.3.cmml">n</mi>
          </mfrac>
        </mstyle>
      </mrow>
      <mo id="p1.1.m1.1.7" xref="p1.1.m1.1.15.1.cmml">,</mo>
      <mrow id="p1.1.m1.1.15.4" xref="p1.1.m1.1.15.4.cmml">
        <msup id="p1.1.m1.1.15.4.2" xref="p1.1.m1.1.15.4.2.cmml">
          <mrow id="p1.1.m1.1.15.4.2.2" xref="p1.1.m1.1.15.4.2.2.2.cmml">
            <mo stretchy="false" id="p1.1.m1.1.8" xref="p1.1.m1.1.15.4.2.2.2.cmml">(</mo>
            <mrow id="p1.1.m1.1.15.4.2.2.2" xref="p1.1.m1.1.15.4.2.2.2.cmml">
              <mo id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">-</mo>
              <mn id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">1</mn>
            </mrow>
            <mo stretchy="false" id="p1.1.m1.1.11" xref="p1.1.m1.1.15.4.2.2.2.cmml">)</mo>
          </mrow>
          <mi id="p1.1.m1.1.12.1" xref="p1.1.m1.1.12.1.cmml">k</mi>
        </msup>
        <mo id="p1.1.m1.1.15.4.1" xref="p1.1.m1.1.15.4.1.cmml"></mo>
        <mi id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">h</mi>
      </mrow>
      <mo id="p1.1.m1.1.14" xref="p1.1.m1.1.15.1.cmml">)</mo>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <vector id="p1.1.m1.1.15.1.cmml" xref="p1.1.m1.1.15">
        <apply id="p1.1.m1.1.15.2.cmml" xref="p1.1.m1.1.15.2">
          <cos id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2"/>
          <apply id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">
            <divide id="p1.1.m1.1.3.1.cmml" xref="p1.1.m1.1.3"/>
            <apply id="p1.1.m1.1.3.2.cmml" xref="p1.1.m1.1.3.2">
              <times id="p1.1.m1.1.3.2.3.cmml" xref="p1.1.m1.1.3.2.3"/>
              <ci id="p1.1.m1.1.3.2.1.cmml" xref="p1.1.m1.1.3.2.1">𝑘</ci>
              <ci id="p1.1.m1.1.3.2.2.cmml" xref="p1.1.m1.1.3.2.2">𝜋</ci>
            </apply>
            <ci id="p1.1.m1.1.3.3.cmml" xref="p1.1.m1.1.3.3">𝑛</ci>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.15.3.cmml" xref="p1.1.m1.1.15.3">
          <sin id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5"/>
          <apply id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">
            <divide id="p1.1.m1.1.6.1.cmml" xref="p1.1.m1.1.6"/>
            <apply id="p1.1.m1.1.6.2.cmml" xref="p1.1.m1.1.6.2">
              <times id="p1.1.m1.1.6.2.3.cmml" xref="p1.1.m1.1.6.2.3"/>
              <ci id="p1.1.m1.1.6.2.1.cmml" xref="p1.1.m1.1.6.2.1">𝑘</ci>
              <ci id="p1.1.m1.1.6.2.2.cmml" xref="p1.1.m1.1.6.2.2">𝜋</ci>
            </apply>
            <ci id="p1.1.m1.1.6.3.cmml" xref="p1.1.m1.1.6.3">𝑛</ci>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.15.4.cmml" xref="p1.1.m1.1.15.4">
          <times id="p1.1.m1.1.15.4.1.cmml" xref="p1.1.m1.1.15.4.1"/>
          <apply id="p1.1.m1.1.15.4.2.cmml" xref="p1.1.m1.1.15.4.2">
            <csymbol cd="ambiguous" id="p1.1.m1.1.15.4.2.1.cmml" xref="p1.1.m1.1.15.4.2">superscript</csymbol>
            <apply id="p1.1.m1.1.15.4.2.2.2.cmml" xref="p1.1.m1.1.15.4.2.2">
              <minus id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9"/>
              <cn type="integer" id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">1</cn>
            </apply>
            <ci id="p1.1.m1.1.12.1.cmml" xref="p1.1.m1.1.12.1">𝑘</ci>
          </apply>
          <ci id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13"></ci>
        </apply>
      </vector>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle\left(\cos{\frac{k\pi}{n}},\sin{\frac{k\pi}{n}},(-1)^{k}h\right)}</annotation>
  </semantics>
</math>

SVG (11.093 KB / 4.103 KB) :

left-parenthesis cosine StartFraction k times pi Over n EndFraction comma sine StartFraction k times pi Over n EndFraction comma left-parenthesis negative 1 right-parenthesis Superscript k Baseline times h right-parenthesis

MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools) rendering

MathML (0 B / 8 B) :

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :


PNG (0 B / 8 B) :


Translations to Computer Algebra Systems

Translation to Maple

In Maple: (cos((k*pi)/(n)), sin((k*pi)/(n)),(- 1)^(k)* h)

Information about the conversion process:

\cos: Cosine; Example: \cos@@{z}

Will be translated to: cos($0)

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/4.14#E2

Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=cos


\sin: Sine; Example: \sin@@{z}

Will be translated to: sin($0)

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/4.14#E1

Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=sin


\pi: Could be the ratio of a circle's circumference to its diameter == Archimedes' constant.

But it is also a Greek letter. Be aware, that this program translated the letter as a normal Greek letter and not as a constant!
Use the DLMF-Macro \cpi to translate \pi as a constant.



Translation to Mathematica

In Mathematica: (Cos[Divide[k*\[Pi],n]], Sin[Divide[k*\[Pi],n]],(- 1)^(k)* h)

Information about the conversion process:

\cos: Cosine; Example: \cos@@{z}

Will be translated to: Cos[$0]

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/4.14#E2

Mathematica: https://reference.wolfram.com/language/ref/Cos.html


\sin: Sine; Example: \sin@@{z}

Will be translated to: Sin[$0]

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/4.14#E1

Mathematica: https://reference.wolfram.com/language/ref/Sin.html


\pi: Could be the ratio of a circle's circumference to its diameter == Archimedes' constant.

But it is also a Greek letter. Be aware, that this program translated the letter as a normal Greek letter and not as a constant!
Use the DLMF-Macro \cpi to translate \pi as a constant.



Similar pages

Calculated based on the variables occurring on the entire Antiprism page

Identifiers

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results