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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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After Thought

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

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Sketch the graphs of y = sin x and y = tan x and some straight lines. Prove some inequalities.


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.