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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 ?

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Sine Problem

In this 'mesh' of sine graphs, one of the graphs is the graph of the sine function. Find the equations of the other graphs to reproduce the pattern.

Degree Ceremony

Age 16 to 18 Challenge Level:
Draw a right-angled triangle with angles $90^\circ$, $(45+x)^\circ$ and $(45-x)^\circ$.

What does Pythagoras' Theorem tell you about these angles?

Use this information to find $ \sin^2 1^\circ + \sin^2 2^\circ + \, \cdots \,+ \sin^2 359 ^\circ + \sin^2 360^\circ$.