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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 ?

Small Steps

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

Squareness

Age 16 to 18
Challenge Level

This problem calls for you to describe and explain the features of the graphs and symmetry arguments will be very useful. First think about the features of the graphs and try to sketch them for yourself, then it may help to use a graphic calculator or graphing software.