Looking at small values of functions. Motivating the existence of the Taylor expansion.
Build up the concept of the Taylor series
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.
Can you sketch this tricky trig function?
Draw graphs of the sine and modulus functions and explain the humps.
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.
Which is larger cos(sin x) or sin(cos x) ? Does this depend on x ?
Two problems about infinite processes where smaller and smaller steps are taken and you have to discover what happens in the limit.
Can you work out the equations of the trig graphs I used to make my pattern?
What does Pythagoras' Theorem tell you about these angles: 90Â°, (45+x)Â° and (45-x)Â° in a triangle?
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?
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?