Degree Ceremony

What does Pythagoras' Theorem tell you about these angles: 90°, (45+x)° and (45-x)° in a triangle?

Loch Ness

Draw graphs of the sine and modulus functions and explain the humps.

Squareness

The family of graphs of x^n + y^n =1 (for even n) includes the circle. Why do the graphs look more and more square as n increases?

Tangled Trig Graphs

Stage: 5 Challenge Level:
What effect does changing the constant $a$ have on the graph $y=\sin(ax)$?