数学 - JavaScript - D3.js - 解析学 - 各種の初等関数 - 三角関数(三角関数の合成、最大値、最小値)

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
• Pythonからはじめる数学入門(参考書籍)

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。

8. 1. 
      $\begin{array}{l}\cos \alpha =\frac{a}{\sqrt{a^2+b^2}}\\ \sin \alpha =\frac{b}{\sqrt{a^2+b^2}}\\ \\ \sqrt{a^2+b^2}\sin \left(\theta +\alpha \right)\\ =\sqrt{a^2+b^2}\left(\sin \theta \cos \alpha +\cos \theta \sin \alpha \right)\\ =a\sin \theta +b\cos \theta \end{array}$
   2. 
      $\begin{array}{l}\cos \beta =\frac{b}{\sqrt{a^2+b^2}}\\ \sin \beta =\frac{-a}{\sqrt{a^2+b^2}}\\ \\ \sqrt{a^2+b^2}\cos \left(\theta +\beta \right)\\ \sqrt{a^2+b^2}\left(\cos \theta \cos \beta -\sin \theta \sin \beta \right)\\ =a\sin \theta +b\cos \theta \end{array}$
9. 
   $\begin{array}{l}f\left(x\right)=\frac{1+\cos 2x}{2}-\sqrt{5}·\frac{\sin 2x}{2}+3·\frac{1-\cos 2x}{2}\\ =2-\frac{1}{2}\left(\sqrt{5}\sin 2x+2\cos 2x\right)\\ =2-\frac{1}{2}\left(3\sin \left(\theta +2x\right)\right)\\ \\ -1\le \sin \alpha \le 1\\ \\ 最大値\frac{7}{2}\\ 最小値\frac{1}{2}\end{array}$

コード(Emacs)

HTML5

<div id="graph0"></div>
<pre id="output0"></pre>
<label for="x1">x1 = </label>
<input id="x1" type="number" value="-5">
<label for="x2">x2 = </label>
<input id="x2" type="number" 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="sample8.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_x1 = document.querySelector('#x1'),
    input_x2 = document.querySelector('#x2'),
    inputs = [input_x1, input_x2],
    p = (x) => pre0.textContent += x + '\n';

let f = (x) => Math.cos(x) ** 2 - Math.sqrt(5) * Math.sin(x) * Math.cos(x) +
    3 * Math.sin(x) ** 2

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

    let x1 = parseFloat(input_x1.value),
        x2 = parseFloat(input_x2.value);
    
    let points = [];

    for (let x = x1; x <= x2; x += 0.001) {
        points.push([x, f(x)]);
    }
    let xscale = d3.scaleLinear()
        .domain([x1, x2])
        .range([padding, width - padding]);
    let ys = points.map((a) => a[1]);
    let yscale = d3.scaleLinear()
        .domain([x1, x2])
        .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);

    let t1 = points.length / 3,
        t2 = t1 * 2;
    
    svg.selectAll('circle')
        .data(points)
        .enter()
        .append('circle')
        .attr('cx', (d) => xscale(d[0]))
        .attr('cy', (d) => yscale(d[1]))
        .attr('r', 1)
        .attr('fill', 'green');

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

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

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

x1 = x2 =