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Find the Mirror Image of a Trigonometry Function on a Graph

When you multiply a trig function by a negative number, all the output values are reversed in sign. The positive values become negative, and the negative values become positive. The effect that this operation has on the graph is that it appears to have a reflection or flip over a horizontal line.

The graph of <i>y</i> = –sin <i>x</i> is the mirror image of <i>y</i> = sin <i>x</i>.
The graph of y = –sin x is the mirror image of y = sin x.

For example, the figure shows the graph of y = –sin x compared to y = sin x. See how the two graphs compare? The original graph appears to be flipped over the x-axis.

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