Trigonometric functions and graphs

There are 16 NRICH Mathematical resources connected to Trigonometric functions and graphs
What's that graph?
problem
Favourite

What's that graph?

Age
14 to 18
Challenge level
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Can you work out which processes are represented by the graphs?

Loch Ness
problem
Favourite

Loch ness

Age
16 to 18
Challenge level
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Draw graphs of the sine and modulus functions and explain the humps.
Squareness
problem
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Squareness

Age
16 to 18
Challenge level
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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?
Sine and Cosine
problem
Favourite

Sine and cosine

Age
14 to 16
Challenge level
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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?
Taking trigonometry series-ly
problem
Favourite

Taking trigonometry series-ly

Age
16 to 18
Challenge level
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Look at the advanced way of viewing sin and cos through their power series.
Tangled Trig Graphs
problem
Favourite

Tangled trig graphs

Age
16 to 18
Challenge level
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Can you work out the equations of the trig graphs I used to make my pattern?

Back fitter
problem
Favourite

Back fitter

Age
14 to 18
Challenge level
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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?

Small Steps
problem

Small steps

Age
16 to 18
Challenge level
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Two problems about infinite processes where smaller and smaller steps are taken and you have to discover what happens in the limit.
Climbing
problem

Climbing

Age
16 to 18
Challenge level
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Sketch the graphs of y = sin x and y = tan x and some straight lines. Prove some inequalities.