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.

After Thought

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

Strange Rectangle 2

Find the exact values of some trig. ratios from this rectangle in which a cyclic quadrilateral cuts off four right angled triangles.

Degree Ceremony

Stage: 5 Challenge Level:

You can draw the graph of the sine function. What about the graph of $y = \sin^2 x$? What about the periodicity of this graph?

What can you say about the angles (45 + x) degrees and (45 - x) degrees, the sines of these angles and the squares of the sines of these angles?