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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

(1) Consider each quadrant separately or use a symmetry argument.

(2) Write $2^{1/n} = 1 + \delta$ and use the Binomial Theorem.

(3) Consider the symmetry of the graph and the point at which it cuts the line $y=x$.

(4) Use the result of (3) and a symmetry argument.

(5) Consider each quadrant separately.