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# Tangled Trig Graphs

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Age 16 to 18

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This anonymous solver correctly identified the remaining curves, and explained how to draw a graph of sin $x$ using the cosine function:

The red graph has equation $y=-\sin x$.

The green graph has equation $y =\sin 2x$.

The light blue graph has equation $y=-\sin 2x$.

The grey graph has equation $y=\sin 3x$.

The dark blue graph has equation $y=-\sin 3x$.

The graph $y=\cos x$ is the same shape as $y=\sin x$ but shifted along. I can make the shape of $y=\sin x$ by drawing the graph $y=\cos (x-90^{\circ})$.

The red graph has equation $y=-\sin x$.

The green graph has equation $y =\sin 2x$.

The light blue graph has equation $y=-\sin 2x$.

The grey graph has equation $y=\sin 3x$.

The dark blue graph has equation $y=-\sin 3x$.

The graph $y=\cos x$ is the same shape as $y=\sin x$ but shifted along. I can make the shape of $y=\sin x$ by drawing the graph $y=\cos (x-90^{\circ})$.

Two problems about infinite processes where smaller and smaller steps are taken and you have to discover what happens in the limit.