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## 'Tangled Trig Graphs' printed from http://nrich.maths.org/

Here is a pattern I made with some graphs of trigonometric
functions.You can find a copy to print

here.
- The purple line is the graph $y=\sin x$. Can you identify the
coordinates of the points where it crosses the axes and where it
reaches its maximum and its minimum values?

- How could I make the red graph from the purple graph? Can you
work out the equation of the red graph?

- The green graph has equation $y=\sin 2x$. Can you describe how
to make the green graph from the purple graph? How does the
transformation of the graph relate to the way the equation has
changed?

- Using these ideas, can you work out the equations of the other
graphs I have drawn?

Imagine you had a graphical calculator but the sine button is
broken. Can you draw the same patterns using the cosine function
instead? Explain how you can transform a cosine graph into a sine
graph.

Why not create some trig patterns of your own using graphical
calculators or graphing software, and send them to us.

This problem is also available in French:

Trigo tricoté