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Small Steps
Two problems about infinite processes where smaller and smaller steps are taken and you have to discover what happens in the limit.
Age 16 to 18
Challenge Level
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 $y=\cos (x-90^{\circ})$.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.