数学 - JavaScript - D3.js - 解析学 - 各種の初等関数 - 三角関数(正接の加法定理)

解析入門〈1〉

学習環境

• Surface 3 (4G LTE)、Surface 3 タイプ カバー、Surface ペン(端末)
• Windows 10 Pro (OS)
• 数式入力ソフト(TeX, MathML): MathType
• MathML対応ブラウザ: Firefox、Safari
• MathML非対応ブラウザ(Internet Explorer, Google Chrome...)用JavaScript Library: MathJax
• 参考書籍
  • JavaScriptリファレンス 第6版
  • インタラクティブ・データビジュアライゼーション

解析入門〈1〉(松坂 和夫(著)、岩波書店)の第5章(各種の初等関数)、5.3(三角関数)、問題5.8、9.を取り組んでみる。

10. 
    $\begin{array}{l}A+B+C=\pi \\ A\le B\le C\\ A\le \frac{\pi }{3}\\ \tan A\le \sqrt{3}\\ \tan A=1\\ A=\frac{\pi }{4}\\ B+C=\pi -\frac{\pi }{4}=\frac{3}{4}\pi \\ \tan \left(B+C\right)=-1\\ \tan \left(B+C\right)=\frac{\tan B+\tan C}{1-\tan B\tan C}\\ \tan B+\tan C=\tan B\tan C-1\\ \tan B\tan C-\tan B-\tan C-1=0\\ \left(\tan B-1\right)\left(\tan C-1\right)-1-1=0\\ \left(\tan B-1\right)\left(\tan C-1\right)=2\\ \tan B-1=1\\ \tan C-1=2\\ \tan B=2\\ \tan C=3\end{array}$
11. 
    $\begin{array}{l}\tan \alpha =\frac{a}{x}\\ \tan \beta =\frac{b}{x}\\ \theta =\alpha -\beta \\ \tan \theta =\tan \left(\alpha -\beta \right)\\ =\frac{\tan \alpha -\tan \beta }{1+\tan \alpha \tan \beta }\\ =\frac{\frac{a-b}{x}}{1+\frac{ab}{x^2}}\\ =\frac{\left(a-b\right)x}{x^2+ab}\\ \\ \frac{\left(x^2+ab\right)-2x^2}{{\left(x^2+ab\right)}^4}\\ =\frac{ab-x^2}{{\left(x^2+ab\right)}^4}\\ x=\sqrt{ab}\end{array}$

コード(Emacs)

HTML5

<div id="graph0"></div>
<pre id="output0"></pre>
<label for="a0">a = </label>
<input id="a0" type="number" min="0.001" value="10">
<label for="b0">b = </label>
<input id="b0" type="number" min="0.001" value="5">
<label for="x0">x = </label>
<input id="x0" type="number" min="0.001" value="5">

<button id="draw0">draw</button>
<button id="clear0">clear</button>

<script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/d3/4.2.6/d3.min.js" integrity="sha256-5idA201uSwHAROtCops7codXJ0vja+6wbBrZdQ6ETQc=" crossorigin="anonymous"></script>

<script src="sample10.js"></script>    

JavaScript

let div0 = document.querySelector('#graph0'),
    pre0 = document.querySelector('#output0'),
    width = 600,
    height = 600,
    padding = 50,
    btn0 = document.querySelector('#draw0'),
    btn1 = document.querySelector('#clear0'),
    input_a0 = document.querySelector('#a0'),
    input_b0 = document.querySelector('#b0'),
    input_x0 = document.querySelector('#x0'),
    inputs = [input_a0, input_b0, input_x0],
    p = (x) => pre0.textContent += x + '\n';

let f = (a, b, x) => Math.atan((a - b) * x / (x **  2 + a * b));

let draw = () => {
    pre0.textContent = '';

    let a = parseFloat(input_a0.value),
        b = parseFloat(input_b0.value),
        x = parseFloat(input_x0.value);

    if (b <= 0 || a <= b || x <= 0) {
        return;
    }

    let points = [[0, a], [0, b]];

    let d = Math.max(a, x);
    let xscale = d3.scaleLinear()
        .domain([0, d])
        .range([padding, width - padding]);
    let yscale = d3.scaleLinear()
        .domain([0, d])
        .range([height - padding, padding]);

    let xaxis = d3.axisBottom().scale(xscale);
    let yaxis = d3.axisLeft().scale(yscale);
    div0.innerHTML = '';
    let svg = d3.select('#graph0')
        .append('svg')
        .attr('width', width)
        .attr('height', height);

    svg.selectAll('line')
        .data(points)
        .enter()
        .append('line')
        .attr('x1', (d) => xscale(d[0]))
        .attr('y1', (d) => yscale(d[1]))
        .attr('x2', xscale(x))
        .attr('y2', yscale(0))
        .attr('stroke', (d, i) => i === 0 ? 'green' : 'blue');

    svg.append('g')
        .attr('transform', `translate(0, ${yscale(0)})`)
        .call(xaxis);

    svg.append('g')
        .attr('transform', `translate(${xscale(0)}, 0)`)
        .call(yaxis);

    p(`θ = ${f(a, b, x)}`);
}

inputs.forEach((input) => input.onchange = draw);
btn0.onclick = draw;
btn1.onclick = () => pre0.textContent = '';
draw();

a = b = x =