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Degree Ceremony

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

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Ball Bearings

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

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After Thought

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

Complex Sine

Age 16 to 18 Challenge Level:
Show that the complex solutions of $\sin z = 2$ are given by $$z = {\pi \over 2} - i \log (2\pm\sqrt 3) +2n\pi.$$