Reflections of trig graphs

Reflections of trig graphs

Understanding Reflections of Trigonometric Graphs

• The reflection of a trigonometric graph is a transformation which flips the graph across a line known as the axis of reflection.
• Reflections downplay the importance of orientation – it’s the mirror image in the ‘water’ reflection analogy.
• Reflections are essentially about flipping the orientation of a graph to produce a mirror image.

Reflections about the x-axis

• A reflection about the x-axis for a sine graph results in the graph being turned upside down. This is represented mathematically as -sin(x).
• A cosine graph reflected about the x-axis is also an upside-down version of the original graph, represented as -cos(x).
• Tangent graphs reflected in the x-axis are opposite in the vertical direction too, represented as -tan(x).

Reflections about the y-axis

• Reflection about the y-axis for a sine graph gives a waveform which starts descending from the origin, represented mathematically as sin(-x).
• A cosine graph mirrored over the y-axis offers a waveform which starts at the minimum (-1), represented as cos(-x).
• Tangent graphs reflected in the y-axis are mirrored over the y-axis, represented as tan(-x).

Practical Tips

• Familiarity with the basic trigonometric graphs helps in understanding their reflections.
• Retain a clear understanding of negative angles and their representations on the graphs.
• Practice graphing these by applying different transformations to get a hands-on understanding of reflections.
• Mastering reflections help in understanding advanced mathematical concepts in trigonometry and calculus.