<p class="paragraph-header">Sketch of Trigonometric Functions with \(a&lt;0\)</p>
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When \(a<0\), the graph is reflected in its midline. Sine and cosine swap their peaks and troughs, while each tangent branch reverses its direction. The amplitude of sine or cosine is the positive distance \(\lvert a\rvert\), and the period is unchanged.

Peaks and troughs swap; period unchanged.

Reflected in the shifted midline; extrema remain \(c\pm\lvert a\rvert\).

Starts at a minimum instead of a maximum; period unchanged.

Branches decrease instead of increase; asymptotes and period are unchanged.

Amplitude is a positive distance. For \(y=2-3\cos 2x\), the amplitude is \(3\), not \(-3\); the minus sign reflects the curve in the midline \(y=2\).

Trigonometry - Trigonometric Functions and Graphs - General

Trigonometry - Trigonometric Functions and Graphs - General

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