Trigonometric functions and graphs

problem
Small steps

Age

16 to 18

Challenge level

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

Age

16 to 18

Challenge level

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

Age

14 to 16

Challenge level

The sine of an angle is equal to the cosine of its complement. Can you explain why and does this rule extend beyond angles of 90 degrees?
problem
Taking trigonometry series-ly

Age

16 to 18

Challenge level

Look at the advanced way of viewing sin and cos through their power series.
problem
Trigger

Age

16 to 18

Challenge level

Can you sketch this tricky trig function?
problem
Squareness

Age

16 to 18

Challenge level

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?
problem
Building approximations for sin(x)

Age

16 to 18

Challenge level

Build up the concept of the Taylor series
problem
Spherical triangles on very big spheres

Age

16 to 18

Challenge level

Shows that Pythagoras for Spherical Triangles reduces to Pythagoras's Theorem in the plane when the triangles are small relative to the radius of the sphere.
problem
Trig-trig

Age

16 to 18

Challenge level

Explore the properties of combinations of trig functions in this open investigation.
problem
Back fitter

Age

14 to 18

Challenge level

10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?