Trigonometric functions and graphs

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?

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

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

Two problems about infinite processes where smaller and smaller steps are taken and you have to discover what happens in the limit.

Which is larger cos(sin x) or sin(cos x) ? Does this depend on x ?

Can you find the sum of the squared sine values?