diff --git a/frontend/js/labs/trigcircle.js b/frontend/js/labs/trigcircle.js
index d609728..4674e03 100644
--- a/frontend/js/labs/trigcircle.js
+++ b/frontend/js/labs/trigcircle.js
@@ -53,6 +53,7 @@ class TrigCircleSim {
this.graphFn = 'sin';
this.snapToNotable = true;
this.animating = false;
+ this.eq = null; // режим уравнения: { fn:'sin'|'cos'|'tg', a:Number, sols:[рад] } | null
this._cx = 0; this._cy = 0; this._r = 0;
this._gx = 0; this._gw = 0; this._gh = 0; this._gy = 0;
@@ -96,6 +97,7 @@ class TrigCircleSim {
this._drawBg(c);
this._drawCircle(c);
+ if (this.eq) this._drawEquation(c);
if (this.showGraph) { this._drawDivider(c); this._drawGraph(c); }
this._drawParticles(c);
if (window.LabFX) LabFX.particles.draw(c);
@@ -116,6 +118,41 @@ class TrigCircleSim {
this._layout(); this.draw();
}
+ /* Режим уравнения: подсветить на окружности все решения fn(x)=a. */
+ setEquation(fn, a, sols) {
+ this.eq = { fn, a, sols: sols || [] };
+ if (this.eq.sols.length) this.angle = this.eq.sols[0]; // встать на первое решение
+ this.draw();
+ }
+ clearEquation() { this.eq = null; this.draw(); }
+
+ _drawEquation(c) {
+ const cx = this._cx, cy = this._cy, r = this._r;
+ const { fn, a, sols } = this.eq;
+ const accent = fn === 'sin' ? _TC.sin : fn === 'cos' ? _TC.cos : _TC.tan;
+ c.save();
+ /* направляющая линия значения */
+ c.strokeStyle = _tcRgba(accent, 0.55); c.lineWidth = 1.5; c.setLineDash([6, 5]);
+ c.beginPath();
+ if (fn === 'sin') { const y = cy - r * a; c.moveTo(cx - r - 22, y); c.lineTo(cx + r + 22, y); }
+ else if (fn === 'cos') { const x = cx + r * a; c.moveTo(x, cy - r - 22); c.lineTo(x, cy + r + 22); }
+ else { const ang = sols.length ? sols[0] : Math.atan(a); const dx = Math.cos(ang), dy = Math.sin(ang), L = r + 24;
+ c.moveTo(cx - L * dx, cy + L * dy); c.lineTo(cx + L * dx, cy - L * dy); }
+ c.stroke(); c.setLineDash([]);
+ /* точки-решения + подписи градусов */
+ c.font = 'bold 11px Manrope,sans-serif';
+ sols.forEach(ang => {
+ const x = cx + r * Math.cos(ang), y = cy - r * Math.sin(ang);
+ c.fillStyle = accent; c.shadowColor = accent; c.shadowBlur = 12;
+ c.beginPath(); c.arc(x, y, 6, 0, Math.PI * 2); c.fill(); c.shadowBlur = 0;
+ c.fillStyle = 'rgba(255,255,255,0.92)'; c.beginPath(); c.arc(x, y, 2.2, 0, Math.PI * 2); c.fill();
+ const lr = r + 18, lx = cx + lr * Math.cos(ang), ly = cy - lr * Math.sin(ang);
+ c.fillStyle = accent; c.textAlign = 'center'; c.textBaseline = 'middle';
+ c.fillText(Math.round(ang * 180 / Math.PI) + '°', lx, ly);
+ });
+ c.restore();
+ }
+
goToAngle(rad) {
this._animTarget = this._norm(rad);
if (!this.animating) this._startAnim();
@@ -1058,6 +1095,80 @@ if (typeof window !== 'undefined') window.TrigCircleSim = TrigCircleSim;
if (fns) fns.style.display = on ? '' : 'none';
}
+ /* ── Уравнения: решения fn(x)=a на [0,2π) ── */
+ function _trigSolveAngles(fn, a) {
+ const TAU = 2 * Math.PI, norm = x => ((x % TAU) + TAU) % TAU;
+ let raw;
+ if (fn === 'sin') { if (Math.abs(a) > 1) return []; const b = Math.asin(a); raw = [b, Math.PI - b]; }
+ else if (fn === 'cos') { if (Math.abs(a) > 1) return []; const b = Math.acos(a); raw = [b, -b]; }
+ else { const b = Math.atan(a); raw = [b, b + Math.PI]; } // tg — всегда есть решения
+ const out = [];
+ raw.map(norm).forEach(x => { if (!out.some(y => Math.abs(y - x) < 1e-6 || Math.abs(y - x - TAU) < 1e-6)) out.push(x); });
+ return out.sort((p, q) => p - q);
+ }
+ /* Радиан → LaTeX красивой π-доли (или null). Покрывает главные значения arcsin/arccos/arctg. */
+ function _radLatex(rad) {
+ const P = Math.PI;
+ const T = [[0, '0'], [P/6, '\\tfrac{\\pi}{6}'], [P/4, '\\tfrac{\\pi}{4}'], [P/3, '\\tfrac{\\pi}{3}'],
+ [P/2, '\\tfrac{\\pi}{2}'], [2*P/3, '\\tfrac{2\\pi}{3}'], [3*P/4, '\\tfrac{3\\pi}{4}'],
+ [5*P/6, '\\tfrac{5\\pi}{6}'], [P, '\\pi']];
+ for (const [v, l] of T) {
+ if (Math.abs(rad - v) < 1e-6) return l;
+ if (v > 0 && Math.abs(rad + v) < 1e-6) return '-' + l;
+ }
+ return null;
+ }
+ /* Общая формула решения (LaTeX) или {none:true}. */
+ function _trigEqFormulaLatex(fn, a) {
+ if ((fn === 'sin' || fn === 'cos') && Math.abs(a) > 1) return { none: true };
+ if (fn === 'sin') {
+ const p = _radLatex(Math.asin(a)) || ('\\arcsin ' + _latexVal(a));
+ return { latex: `x = (-1)^{n}\\,${p} + \\pi n,\\ n\\in\\mathbb{Z}` };
+ }
+ if (fn === 'cos') {
+ const p = _radLatex(Math.acos(a)) || ('\\arccos ' + _latexVal(a));
+ return { latex: `x = \\pm ${p} + 2\\pi n,\\ n\\in\\mathbb{Z}` };
+ }
+ const p = _radLatex(Math.atan(a)) || ('\\operatorname{arctg} ' + _latexVal(a));
+ return { latex: `x = ${p} + \\pi n,\\ n\\in\\mathbb{Z}` };
+ }
+
+ var trigEqFn = 'sin';
+ function trigSetEqFn(fn, btn) {
+ trigEqFn = fn;
+ document.querySelectorAll('.trig-eq-fn').forEach(b => b.classList.remove('active'));
+ if (btn) btn.classList.add('active');
+ }
+ function trigSolve() {
+ if (!trigSim) return;
+ const inp = document.getElementById('trig-eq-input');
+ const a = parseFloat(String(inp && inp.value || '').replace(',', '.'));
+ const fnTex = { sin: '\\sin', cos: '\\cos', tg: '\\operatorname{tg}' }[trigEqFn];
+ const fEl = document.getElementById('trig-eq-formula');
+ const sEl = document.getElementById('trig-eq-sols');
+ if (!isFinite(a)) { if (fEl) fEl.innerHTML = 'Введите значение a'; if (sEl) sEl.textContent = ''; return; }
+ const sols = _trigSolveAngles(trigEqFn, a);
+ trigSim.setEquation(trigEqFn, a, sols);
+ const K = window.katex;
+ const tex = l => (K ? K.renderToString(l, { throwOnError: false, strict: false, displayMode: false }) : l);
+ const eqHead = tex(`${fnTex} x = ${_latexVal(a)}`);
+ const f = _trigEqFormulaLatex(trigEqFn, a);
+ if (fEl) {
+ fEl.innerHTML = `${eqHead}
` +
+ (f.none ? 'Нет решений (|a| > 1)
' : `${tex(f.latex)}
`);
+ }
+ if (sEl) sEl.textContent = sols.length
+ ? 'На [0, 2π): ' + sols.map(x => Math.round(x * 180 / Math.PI) + '°').join(', ')
+ : '';
+ }
+ function trigClearEq() {
+ if (!trigSim) return;
+ trigSim.clearEquation();
+ const fEl = document.getElementById('trig-eq-formula'); if (fEl) fEl.innerHTML = '';
+ const sEl = document.getElementById('trig-eq-sols'); if (sEl) sEl.textContent = '';
+ }
+ function trigEqKey(e) { if (e && (e.key === 'Enter' || e.keyCode === 13)) trigSolve(); }
+
function _trigUpdateUI(s) {
const _f = v => {
if (v === undefined) return '—';
diff --git a/frontend/labs-bodies.html b/frontend/labs-bodies.html
index 9a4ed74..9dcffdd 100644
--- a/frontend/labs-bodies.html
+++ b/frontend/labs-bodies.html
@@ -582,6 +582,23 @@
Точные значения · приведение
—
+
+ Уравнение
+
+
+
+
+ x =
+
+
+
+
+
+
+
+
+
Табличные углы