2017年5月2日火曜日

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5.3-5.を取り組んでみる。


  1. sin( π 2 θ ) =sin π 2 cosθcos π 2 sinθ =cosθ cos( π 2 θ ) =cos π 2 cosθ+sin π 2 sinθ =sinθ

  2. sin( πθ ) =sinπcosθcosπsinθ =sinθ cos( πθ ) =cosπcosθ+sinπsinθ =cosθ

  3. sin2α =sin( α+α ) =sinαcosα+cosαsinα =2sinαcosα cos2α =cos( α+α ) =cosαcosαsinαsinα = cos 2 α sin 2 α = cos 2 α( 1 cos 2 α ) =2 cos 2 α1 =2( 1 sin 2 α )1 =12 sin 2 α tan2α =tan( α+α ) = tanα+tanα 1tanαtanα = 2tanα 1 tan 2 α

  4. sin 2 α 2 = 1 2 ( 1cos2· α 2 ) = 1cosα 2 cos 2 α 2 = cos2· α 2 +1 2 = 1+cosα 2

  5. sin3α =sin( α+2α ) =sinαcos2α+cosαsin2α =sinα( cos 2 α sin 2 α )+cosα( sinαcosα+cosαsinα ) =sinα cos 2 α sin 3 α+sinα cos 2 α+sinα cos 2 α =3sinα cos 2 α sin 3 α =3sinα( 1 sin 2 α ) sin 3 α =3sinα4 sin 3 α cos3α =cos( α+2α ) =cosαcos2αsinαsin2α =cosα( cos 2 α sin 2 α )sinα( 2sinαcosα ) =cosα( cos 2 α( 1 cos 2 α ) )2 sin 2 αcosα =2 cos 3 αcosα2( 1 cos 2 α )cosα =4 cos 3 α3cosα

コード(Emacs)

HTML5

<div id="graph0"></div>
<pre id="output0"></pre>
<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="sample1.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'),
    p = (x) => pre0.textContent += x + '\n';

let f = (x) => Math.sin(3 * x),
    g = (x) => 3 * Math.sin(x) - 4 * Math.sin(x) ** 3;

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

    for (let x = -Math.PI; x <= Math.PI; x += 0.001) {
        points.push([x, f(x)]);
    }
    for (let x = -Math.PI; x <= Math.PI; x += 0.001) {
        points.push([x, g(x)]);
    }
    for (let x = -Math.PI; x <= Math.PI; x += 0.001) {
        points.push([x, Math.sin(x)]);
    }
    let xscale = d3.scaleLinear()
        .domain([-Math.PI, Math.PI])
        .range([padding, width - padding]);
    let ys = points.map((a) => a[1]);
    let yscale = d3.scaleLinear()
        .domain([-Math.PI, Math.PI])
        .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', (d, i) => i < t1 ? 4 : 1)
        .attr('fill', (d, i) =>
              i < t1 ? 'green' :
              i < t2 ? 'blue' : 'red');

    svg.append('g')
        .attr('transform', `translate(0, ${height / 2})`)
        .call(xaxis);

    svg.append('g')
        .attr('transform', `translate(${width / 2}, 0)`)
        .call(yaxis);
}

btn0.onclick = draw;
btn1.onclick = () => pre0.textContent = '';
draw();






  







 
						

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