2017年5月8日月曜日

学習環境

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。


    1. cosα= a a 2 + b 2 sinα= b a 2 + b 2 a 2 + b 2 sin( θ+α ) = a 2 + b 2 ( sinθcosα+cosθsinα ) =asinθ+bcosθ

    2. cosβ= b a 2 + b 2 sinβ= a a 2 + b 2 a 2 + b 2 cos( θ+β ) a 2 + b 2 ( cosθcosβsinθsinβ ) =asinθ+bcosθ

  1. f( x )= 1+cos2x 2 5 · sin2x 2 +3· 1cos2x 2 =2 1 2 ( 5 sin2x+2cos2x ) =2 1 2 ( 3sin( θ+2x ) ) 1sinα1 7 2 1 2

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();
























						

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