Degree Ceremony

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 ?

Climbing

Sketch the graphs of y = sin x and y = tan x and some straight lines. Prove some inequalities.

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