Build up the concept of the Taylor series
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Look at the advanced way of viewing sin and cos through their power series.
Explore the properties of combinations of trig functions in this open investigation.
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.
What does Pythagoras' Theorem tell you about these angles: 90°, (45+x)° and (45-x)° in a triangle?
Draw graphs of the sine and modulus functions and explain the humps.
Can you sketch this tricky trig function?
Which is larger cos(sin x) or sin(cos x) ? Does this depend on x ?
Can you work out the equations of the trig graphs I used to make my pattern?
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?
Sketch the graphs of y = sin x and y = tan x and some straight lines. Prove some inequalities.
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?