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線型代数入門 (松坂 和夫(著)、岩波書店)の第4章(複素数、複素ベクトル空間)、3(極形式)、問4.を取り組んでみる。
問4.
JavaScriptで確認してみる。
HTML5
<label for="varphi0">
φ =
</label>
<input id="varphi0" type="number" min="0.01" step="0.01" value="0.5">
<br>
cos 3φ = <span id="answer00"></span><br>
cos^2 φ - 3cos φ sin^2 φ = <span id="answer01"></span><br>
差: <span id="diff0"></span><br>
sin 4φ = <span id="answer10"></span><br>
4cos^3 φ sin φ - 4 cos φ sin^3 φ = <span id="answer11"></span><br>
差: <span id="diff1"></span><br>
cos 5φ = <span id="answer20"></span><br>
cos^5 φ - 10cos^3 φ sin^2 φ + 5 cos φ sin^4 φ = <span id="answer21"></span><br>
差: <span id="diff2"></span><br>
<script src="sample4.js"></script>
JavaScript
コード(Emacs)
(function () {
'use strict';
var input_varphi = document.querySelector('#varphi0'),
span_answer00 = document.querySelector('#answer00'),
span_answer01 = document.querySelector('#answer01'),
span_diff0 = document.querySelector('#diff0'),
span_answer10 = document.querySelector('#answer10'),
span_answer11 = document.querySelector('#answer11'),
span_diff1 = document.querySelector('#diff1'),
span_answer20 = document.querySelector('#answer20'),
span_answer21 = document.querySelector('#answer21'),
span_diff2 = document.querySelector('#diff2'),
calc0,
calc1,
calc2,
cos,
sin,
output;
calc0 = function (c, s) {
return Math.pow(c, 3) - 3 * c * Math.pow(s, 2);
};
calc1 = function (c, s) {
return 4 * Math.pow(c, 3) * s - 4 * c * Math.pow(s, 3);
};
calc2 = function (c, s) {
return Math.pow(c, 5) - 10 * Math.pow(c, 3) * Math.pow(s, 2) +
5 * c * Math.pow(s, 4);
};
output = function () {
var varphi = parseFloat(input_varphi.value),
cos = Math.cos(varphi),
sin = Math.sin(varphi),
a00 = Math.cos(3 * varphi),
a01 = calc0(cos, sin),
a10 = Math.sin(4 * varphi),
a11 = calc1(cos, sin),
a20 = Math.cos(5 * varphi),
a21 = calc2(cos, sin);
span_answer00.innerText = a00;
span_answer01.innerText = a01;
span_diff0.innerText = a00 - a01;
span_answer10.innerText = a10;
span_answer11.innerText = a11;
span_diff1.innerText = a10 - a11;
span_answer20.innerText = a20;
span_answer21.innerText = a21;
span_diff2.innerText = a20 - a21;
};
input_varphi.onchange = output;
output();
}());
cos 3φ =
cos^2 φ - 3cos φ sin^2 φ =
差:
sin 4φ =
4cos^3 φ sin φ - 4 cos φ sin^3 φ =
差:
cos 5φ =
cos^5 φ - 10cos^3 φ sin^2 φ + 5 cos φ sin^4 φ =
差:
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