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<!DOCTYPE html>
<html lang="zh-Hant">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>sin / cos 數值對照 · 單位圓</title>
<link rel="preconnect" href="https://fonts.googleapis.com">
<link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
<link href="https://fonts.googleapis.com/css2?family=Fraunces:opsz,wght@9..144,500;9..144,600&family=IBM+Plex+Mono:wght@400;500;600&family=Noto+Sans+TC:wght@400;500;700&display=swap" rel="stylesheet">
<style>
:root{
--bg:#0d1a2b;
--bg2:#0a1421;
--surface:#16273d;
--surface2:#1b3048;
--line:#2a405d;
--ink:#eaf1f8;
--muted:#8399b3;
--cos:#46c9b8; /* 水平 → cos */
--sin:#f5b13d; /* 垂直 → sin */
--point:#ff6b7a;
}
*{box-sizing:border-box;margin:0;padding:0}
html{-webkit-text-size-adjust:100%}
body{
background:
radial-gradient(1200px 600px at 80% -10%, #16273d 0%, transparent 60%),
var(--bg);
color:var(--ink);
font-family:"Noto Sans TC","Inter",system-ui,sans-serif;
line-height:1.6;
padding:clamp(20px,4vw,56px);
min-height:100vh;
}
.wrap{max-width:980px;margin:0 auto}
header{margin-bottom:clamp(28px,4vw,44px)}
.eyebrow{
font-family:"IBM Plex Mono",monospace;
font-size:12px;letter-spacing:.28em;text-transform:uppercase;
color:var(--muted);margin-bottom:14px;
}
h1{
font-family:"Fraunces",serif;
font-weight:600;
font-size:clamp(34px,7vw,60px);
line-height:1.02;letter-spacing:-.01em;
}
h1 .s{color:var(--sin)}
h1 .c{color:var(--cos)}
.lede{color:var(--muted);max-width:52ch;margin-top:14px;font-size:15px}
/* ---- 主要互動區 ---- */
.stage{
display:grid;grid-template-columns:minmax(0,1fr) 300px;gap:22px;
align-items:stretch;margin-bottom:26px;
}
.card{
background:linear-gradient(180deg,var(--surface),var(--bg2));
border:1px solid var(--line);border-radius:18px;
padding:22px;
}
.circle-card{display:flex;align-items:center;justify-content:center;position:relative}
svg{width:100%;height:auto;display:block;touch-action:none;max-width:440px}
.hint{
position:absolute;bottom:14px;left:0;right:0;text-align:center;
font-family:"IBM Plex Mono",monospace;font-size:11px;color:var(--muted);
letter-spacing:.04em;pointer-events:none;
}
/* ---- 讀值面板 ---- */
.readout{display:flex;flex-direction:column;gap:14px}
.angle-big{
font-family:"IBM Plex Mono",monospace;
font-size:40px;font-weight:600;line-height:1;
}
.angle-rad{font-family:"IBM Plex Mono",monospace;color:var(--muted);font-size:15px;margin-top:6px}
.val{
border-top:1px solid var(--line);padding-top:12px;
display:flex;align-items:baseline;justify-content:space-between;gap:10px;
}
.val .k{font-family:"IBM Plex Mono",monospace;font-weight:600;font-size:15px;letter-spacing:.02em}
.val .v{font-family:"IBM Plex Mono",monospace;font-size:20px;font-weight:500;text-align:right}
.k.sin,.v.sin{color:var(--sin)}
.k.cos,.v.cos{color:var(--cos)}
.k.tan,.v.tan{color:var(--ink)}
.val .exact{display:block;font-size:12px;color:var(--muted);font-weight:400}
/* ---- 對照表 ---- */
.table-title{
font-family:"IBM Plex Mono",monospace;font-size:12px;letter-spacing:.22em;
text-transform:uppercase;color:var(--muted);margin:8px 4px 12px;
}
.table-scroll{overflow-x:auto;border:1px solid var(--line);border-radius:18px}
table{width:100%;border-collapse:collapse;min-width:520px;font-size:14px}
thead th{
font-family:"IBM Plex Mono",monospace;font-weight:600;font-size:12px;
letter-spacing:.06em;text-transform:uppercase;color:var(--muted);
text-align:right;padding:14px 16px;background:var(--bg2);
position:sticky;top:0;white-space:nowrap;
}
thead th:first-child{text-align:left}
tbody td{
padding:11px 16px;text-align:right;font-family:"IBM Plex Mono",monospace;
border-top:1px solid var(--line);white-space:nowrap;
}
tbody td:first-child{text-align:left;font-weight:600}
tbody td.rad{color:var(--muted)}
tbody td.sc-sin{color:var(--sin)}
tbody td.sc-cos{color:var(--cos)}
tbody tr{cursor:pointer;transition:background .12s}
tbody tr:hover{background:var(--surface)}
tbody tr.active{background:var(--surface2)}
tbody tr.active td:first-child{box-shadow:inset 3px 0 0 var(--point)}
.legend{display:flex;gap:20px;flex-wrap:wrap;margin:16px 4px 0;font-size:13px;color:var(--muted)}
.legend span{display:inline-flex;align-items:center;gap:7px}
.dot{width:11px;height:11px;border-radius:3px;display:inline-block}
.dot.sin{background:var(--sin)}
.dot.cos{background:var(--cos)}
footer{margin-top:28px;color:var(--muted);font-size:12.5px;line-height:1.7}
footer code{font-family:"IBM Plex Mono",monospace;color:var(--ink)}
@media (max-width:760px){
.stage{grid-template-columns:1fr}
.readout{flex-direction:row;flex-wrap:wrap;align-items:center}
.readout .heading{width:100%}
.val{flex:1 1 140px;border-top:none;border-left:1px solid var(--line);padding:0 0 0 14px}
}
</style>
</head>
<body>
<div class="wrap">
<header>
<div class="eyebrow">單位圓 · 三角函數</div>
<h1><span class="s">sin</span> 與 <span class="c">cos</span> 的數值</h1>
<p class="lede">拖曳圓上的紅點，或點選下方表格的任一角度。垂直投影就是 <span style="color:var(--sin)">sin</span>、水平投影就是 <span style="color:var(--cos)">cos</span>——顏色直接對應到坐標軸。</p>
</header>
<div class="stage">
<div class="card circle-card">
<svg id="circle" viewBox="0 0 400 400" role="img" aria-label="可拖曳的單位圓" tabindex="0">
<!-- 格線圈 -->
<circle cx="200" cy="200" r="150" fill="none" stroke="var(--line)" stroke-width="1.5"/>
<!-- 坐標軸 -->
<line x1="30" y1="200" x2="370" y2="200" stroke="var(--line)" stroke-width="1"/>
<line x1="200" y1="30" x2="200" y2="370" stroke="var(--line)" stroke-width="1"/>
<!-- cos 投影（水平）-->
<line id="cosSeg" x1="200" y1="200" x2="350" y2="200" stroke="var(--cos)" stroke-width="4" stroke-linecap="round"/>
<!-- sin 投影（垂直）-->
<line id="sinSeg" x1="350" y1="200" x2="350" y2="200" stroke="var(--sin)" stroke-width="4" stroke-linecap="round"/>
<!-- 半徑 -->
<line id="radius" x1="200" y1="200" x2="350" y2="200" stroke="var(--ink)" stroke-width="1.5" stroke-dasharray="4 4" opacity=".7"/>
<!-- 角度弧 -->
<path id="arc" fill="none" stroke="var(--point)" stroke-width="2.5"/>
<!-- 特殊角小點 -->
<g id="dots"></g>
<!-- 動點 -->
<circle id="point" cx="350" cy="200" r="8" fill="var(--point)" stroke="var(--bg)" stroke-width="2.5"/>
</svg>
<div class="hint">拖曳紅點 · 或用 ← → 方向鍵</div>
</div>
<div class="card readout">
<div class="heading">
<div class="angle-big"><span id="degOut">45</span>°</div>
<div class="angle-rad" id="radOut">π/4 rad</div>
</div>
<div class="val">
<span class="k sin">sin θ</span>
<span class="v sin"><span id="sinOut">0.7071</span><span class="exact" id="sinExact">= √2⁄2</span></span>
</div>
<div class="val">
<span class="k cos">cos θ</span>
<span class="v cos"><span id="cosOut">0.7071</span><span class="exact" id="cosExact">= √2⁄2</span></span>
</div>
<div class="val">
<span class="k tan">tan θ</span>
<span class="v tan"><span id="tanOut">1.0000</span><span class="exact" id="tanExact">= 1</span></span>
</div>
</div>
</div>
<div class="table-title">常見角度對照表</div>
<div class="table-scroll">
<table>
<thead>
<tr><th>角度</th><th>弧度</th><th>sin</th><th>cos</th><th>tan</th></tr>
</thead>
<tbody id="tbody"></tbody>
</table>
</div>
<div class="legend">
<span><i class="dot sin"></i> sin θ ＝ 垂直分量（y 坐標）</span>
<span><i class="dot cos"></i> cos θ ＝ 水平分量（x 坐標）</span>
</div>
<footer>
小提醒：<code>tan θ = sin θ ⁄ cos θ</code>。當 cos θ = 0（也就是 90° 與 270°）時，tan 沒有定義。表格裡的「√2⁄2」也常寫成「1⁄√2」，兩者相等。
</footer>
</div>
<script>
(function(){
const R=150, CX=200, CY=200;
const svg=document.getElementById('circle');
const pt=document.getElementById('point');
const cosSeg=document.getElementById('cosSeg');
const sinSeg=document.getElementById('sinSeg');
const radius=document.getElementById('radius');
const arc=document.getElementById('arc');
const dotsG=document.getElementById('dots');
const tbody=document.getElementById('tbody');
const degOut=document.getElementById('degOut');
const radOut=document.getElementById('radOut');
const sinOut=document.getElementById('sinOut');
const cosOut=document.getElementById('cosOut');
const tanOut=document.getElementById('tanOut');
const sinExact=document.getElementById('sinExact');
const cosExact=document.getElementById('cosExact');
const tanExact=document.getElementById('tanExact');
// 特殊角資料（弧度、精確值皆為顯示字串）
const specials=[
{deg:0, rad:'0', sin:'0', cos:'1', tan:'0'},
{deg:30, rad:'π/6', sin:'1/2', cos:'√3/2', tan:'√3/3'},
{deg:45, rad:'π/4', sin:'√2/2', cos:'√2/2', tan:'1'},
{deg:60, rad:'π/3', sin:'√3/2', cos:'1/2', tan:'√3'},
{deg:90, rad:'π/2', sin:'1', cos:'0', tan:'未定義'},
{deg:120, rad:'2π/3', sin:'√3/2', cos:'−1/2', tan:'−√3'},
{deg:135, rad:'3π/4', sin:'√2/2', cos:'−√2/2',tan:'−1'},
{deg:150, rad:'5π/6', sin:'1/2', cos:'−√3/2',tan:'−√3/3'},
{deg:180, rad:'π', sin:'0', cos:'−1', tan:'0'},
{deg:210, rad:'7π/6', sin:'−1/2', cos:'−√3/2',tan:'√3/3'},
{deg:225, rad:'5π/4', sin:'−√2/2',cos:'−√2/2',tan:'1'},
{deg:240, rad:'4π/3', sin:'−√3/2',cos:'−1/2', tan:'√3'},
{deg:270, rad:'3π/2', sin:'−1', cos:'0', tan:'未定義'},
{deg:300, rad:'5π/3', sin:'−√3/2',cos:'1/2', tan:'−√3'},
{deg:315, rad:'7π/4', sin:'−√2/2',cos:'√2/2', tan:'−1'},
{deg:330, rad:'11π/6', sin:'−1/2', cos:'√3/2', tan:'−√3/3'},
{deg:360, rad:'2π', sin:'0', cos:'1', tan:'0'},
];
// 建立表格
specials.forEach((s,i)=>{
if(s.deg===360) return; // 360 與 0 同值，表格省略避免重複
const tr=document.createElement('tr');
tr.dataset.deg=s.deg;
tr.innerHTML=`<td>${s.deg}°</td>
<td class="rad">${s.rad}</td>
<td class="sc-sin">${s.sin}</td>
<td class="sc-cos">${s.cos}</td>
<td>${s.tan}</td>`;
tr.addEventListener('click',()=>setAngle(s.deg,true));
tbody.appendChild(tr);
});
// 建立圓上特殊角小點
specials.forEach(s=>{
if(s.deg===360) return;
const r=s.deg*Math.PI/180;
const x=CX+R*Math.cos(r), y=CY-R*Math.sin(r);
const c=document.createElementNS('http://www.w3.org/2000/svg','circle');
c.setAttribute('cx',x); c.setAttribute('cy',y); c.setAttribute('r',4);
c.setAttribute('fill','var(--line)');
c.style.cursor='pointer';
c.addEventListener('click',()=>setAngle(s.deg,true));
dotsG.appendChild(c);
});
function fmt(n){ // 4 位小數，處理 -0
if(Math.abs(n)<1e-10) n=0;
return n.toFixed(4);
}
function findExact(deg){
return specials.find(s=>s.deg===((deg%360)+360)%360);
}
function setAngle(deg, snap){
// 圓弧繪製角度用連續值，讀值用四捨五入到 1 度
const dRound=Math.round(deg);
const r=deg*Math.PI/180;
const sinV=Math.sin(r), cosV=Math.cos(r);
const px=CX+R*cosV, py=CY-R*sinV;
pt.setAttribute('cx',px); pt.setAttribute('cy',py);
radius.setAttribute('x2',px); radius.setAttribute('y2',py);
cosSeg.setAttribute('x2',px); // 中心 → (px, CY)
sinSeg.setAttribute('x1',px); sinSeg.setAttribute('x2',px);
sinSeg.setAttribute('y1',CY); sinSeg.setAttribute('y2',py);
// 角度弧（用折線近似，避免大弧旗標麻煩）
let d=`M ${CX+34} ${CY}`;
const steps=Math.max(1,Math.round(Math.abs(deg)/3));
for(let i=1;i<=steps;i++){
const t=(deg*i/steps)*Math.PI/180;
d+=` L ${CX+34*Math.cos(t)} ${CY-34*Math.sin(t)}`;
}
arc.setAttribute('d',d);
// 讀值
degOut.textContent=dRound;
const ex=findExact(dRound);
radOut.textContent=(ex? ex.rad : (r/Math.PI).toFixed(3)+'π')+' rad';
sinOut.textContent=fmt(sinV);
cosOut.textContent=fmt(cosV);
if(Math.abs(cosV)<1e-9){ tanOut.textContent='未定義'; }
else { tanOut.textContent=fmt(sinV/cosV); }
if(ex){
sinExact.textContent='= '+ex.sin; sinExact.style.display='block';
cosExact.textContent='= '+ex.cos; cosExact.style.display='block';
tanExact.textContent='= '+ex.tan; tanExact.style.display='block';
}else{
sinExact.style.display='none';
cosExact.style.display='none';
tanExact.style.display='none';
}
// 表格高亮
[...tbody.children].forEach(tr=>{
tr.classList.toggle('active', parseInt(tr.dataset.deg)===((dRound%360)+360)%360);
});
current=deg;
}
let current=45;
// 拖曳
let dragging=false;
function angleFromEvent(e){
const rect=svg.getBoundingClientRect();
const sx=(e.clientX-rect.left)/rect.width*400;
const sy=(e.clientY-rect.top)/rect.height*400;
let a=Math.atan2(CY-sy, sx-CX)*180/Math.PI; // 數學方向
if(a<0) a+=360;
return a;
}
function start(e){dragging=true; svg.setPointerCapture&&svg.setPointerCapture(e.pointerId); move(e);}
function move(e){ if(!dragging) return; setAngle(angleFromEvent(e),false); e.preventDefault(); }
function end(){dragging=false;}
svg.addEventListener('pointerdown',start);
svg.addEventListener('pointermove',move);
svg.addEventListener('pointerup',end);
svg.addEventListener('pointercancel',end);
// 鍵盤
svg.addEventListener('keydown',e=>{
if(e.key==='ArrowRight'||e.key==='ArrowUp'){ setAngle((Math.round(current)+ (e.shiftKey?15:1))%360,false); e.preventDefault(); }
if(e.key==='ArrowLeft'||e.key==='ArrowDown'){ setAngle(((Math.round(current)-(e.shiftKey?15:1))%360+360)%360,false); e.preventDefault(); }
});
setAngle(45,true);
})();
</script>
</body>
</html>