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What does Pythagoras' Theorem tell you about these angles: 90°, (45+x)° and (45-x)° in a triangle?

After Thought

Which is larger cos(sin x) or sin(cos x) ? Does this depend on x ?

Small Steps

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

Tangled Trig Graphs

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 $y=\cos (x-90^{\circ})$.