### 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 ?

### Climbing

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.