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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 ?


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


Age 16 to 18 Challenge Level:

This problem calls for you to describe and explain the features of the graphs and symmetry arguments will be very useful. First think about the features of the graphs and try to sketch them for yourself, then it may help to use a graphic calculator or graphing software.