### Degree Ceremony

What does Pythagoras' Theorem tell you about these angles: 90Â°, (45+x)Â° and (45-x)Â° 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 18Challenge 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 $y=\cos (x-90^{\circ})$.