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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.

Loch Ness

Age 16 to 18 Challenge Level:

Remember that the function $f(x) = |x|$ is defined as:

$$\eqalign{ y &= x \ {\rm for } \ x\geq 0 \cr &= -x \ {\rm for } \ x < 0 .}$$

Split up the domain of the function.