Trigonometric functions and graphs

problem
Favourite

Taking Trigonometry Series-Ly

Age

16 to 18

Challenge level

2 out of 3

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

Squareness

Age

16 to 18

Challenge level

3 out of 3

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?
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Favourite

Sine and Cosine

Age

14 to 16

Challenge level

1 out of 3

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
Favourite

Back Fitter

Age

14 to 18

Challenge level

2 out of 3

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?
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Favourite

What's That Graph?

Age

14 to 18

Challenge level

2 out of 3

Can you work out which processes are represented by the graphs?
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Favourite

Tangled Trig Graphs

Age

16 to 18

Challenge level

1 out of 3

Can you work out the equations of the trig graphs I used to make my pattern?
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Favourite

Loch Ness

Age

16 to 18

Challenge level

2 out of 3

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

Age

16 to 18

Challenge level

1 out of 3

Two problems about infinite processes where smaller and smaller steps are taken and you have to discover what happens in the limit.
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Building Approximations for Sin(x)

Age

16 to 18

Challenge level

3 out of 3

Build up the concept of the Taylor series
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Spherical Triangles on Very Big Spheres

Age

16 to 18

Challenge level

3 out of 3

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.