diff --git a/frontend/js/labs/trigcircle.js b/frontend/js/labs/trigcircle.js
index 0af8ea6..8d7db74 100644
--- a/frontend/js/labs/trigcircle.js
+++ b/frontend/js/labs/trigcircle.js
@@ -54,6 +54,7 @@ class TrigCircleSim {
this.snapToNotable = true;
this.animating = false;
this.eq = null; // режим уравнения: { fn:'sin'|'cos'|'tg', a:Number, sols:[рад] } | null
+ this.showParity = false; // показать зеркальную точку −α (чётность/нечётность)
this._cx = 0; this._cy = 0; this._r = 0;
this._gx = 0; this._gw = 0; this._gh = 0; this._gy = 0;
@@ -98,6 +99,7 @@ class TrigCircleSim {
this._drawBg(c);
this._drawCircle(c);
if (this.eq) this._drawEquation(c);
+ if (this.showParity) this._drawParity(c);
if (this.showGraph) { this._drawDivider(c); this._drawGraph(c); }
this._drawParticles(c);
if (window.LabFX) LabFX.particles.draw(c);
@@ -153,6 +155,22 @@ class TrigCircleSim {
c.restore();
}
+ /* Зеркальная точка −α (отражение через ось Ox): наглядно чётность cos и нечётность sin. */
+ _drawParity(c) {
+ const cx = this._cx, cy = this._cy, r = this._r, a = this.angle;
+ const px = cx + r * Math.cos(a), py = cy - r * Math.sin(a);
+ const mx = cx + r * Math.cos(-a), my = cy - r * Math.sin(-a);
+ c.save();
+ c.strokeStyle = _tcRgba(_TC.violet, 0.4); c.setLineDash([4, 4]); c.lineWidth = 1;
+ c.beginPath(); c.moveTo(px, py); c.lineTo(mx, my); c.stroke(); c.setLineDash([]);
+ c.strokeStyle = _TC.violet; c.lineWidth = 2; c.fillStyle = 'rgba(155,93,229,0.15)';
+ c.beginPath(); c.arc(mx, my, 6, 0, Math.PI * 2); c.fill(); c.stroke();
+ c.font = 'bold 11px Manrope,sans-serif'; c.fillStyle = _TC.violet;
+ c.textAlign = 'center'; c.textBaseline = 'middle';
+ c.fillText('-α', mx + (Math.cos(-a) >= 0 ? 14 : -14), my);
+ c.restore();
+ }
+
goToAngle(rad) {
this._animTarget = this._norm(rad);
if (!this.animating) this._startAnim();
@@ -1194,6 +1212,25 @@ if (typeof window !== 'undefined') window.TrigCircleSim = TrigCircleSim;
else el.style.display = 'none';
}
+ /* ── Чётность/нечётность + периоды (статический KaTeX-блок, строится один раз) ── */
+ function trigToggleParity(rowEl) {
+ if (!trigSim) return;
+ const on = rowEl.classList.toggle('active');
+ trigSim.showParity = on;
+ trigSim.draw();
+ const pEl = document.getElementById('trig-parity');
+ if (!pEl) return;
+ pEl.style.display = on ? '' : 'none';
+ if (on && !pEl.dataset.built) {
+ pEl.innerHTML =
+ `${_tex('\\sin(-\\alpha) = -\\sin\\alpha')}
` +
+ `${_tex('\\cos(-\\alpha) = \\cos\\alpha')}
` +
+ `${_tex('\\operatorname{tg}(-\\alpha) = -\\operatorname{tg}\\alpha')}
` +
+ `${_tex('T_{\\sin}=T_{\\cos}=2\\pi,\\quad T_{\\operatorname{tg}}=T_{\\operatorname{ctg}}=\\pi')}
`;
+ pEl.dataset.built = '1';
+ }
+ }
+
function _trigUpdateUI(s) {
const _f = v => {
if (v === undefined) return '—';
diff --git a/frontend/labs-bodies.html b/frontend/labs-bodies.html
index f736cc1..ed2a4a4 100644
--- a/frontend/labs-bodies.html
+++ b/frontend/labs-bodies.html
@@ -608,6 +608,15 @@
+
+
+
+
Табличные углы