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Degree Ceremony
What does Pythagoras' Theorem tell you about these angles: 90°, (45+x)° and (45-x)° in a triangle?
Climbing
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.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.