Reflecting Sine and Cosine Functions Across Vertical Lines

Reflecting Sine and Cosine Functions Across Vertical Lines
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2012-07-03 08:18
This applet demonstrates how the graphs of the sine and cosine functions change when reflected across various vertical lines. It covers core concepts such as trigonometric function graphs, geometric transformations (reflection), periodicity, and symmetry. Construction uses the GeoGebra Line command to create vertical lines (objects a, b, c) and the Mirror command to reflect function objects f and g, producing reflected functions f_1 and g_1, with text objects text1 and text2 for annotation. Suitable for high‑school trigonometry lessons, pre‑calculus courses, and independent exploration to visualize the effect of reflections on trigonometric graphs.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Mirror(f, a) → f_1
  3. Mirror(g, a) → g_1