### 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:
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 $\sin^2 1^\circ + \sin^2 2^\circ + \, \cdots \,+ \sin^2 359 ^\circ + \sin^2 360^\circ$.