NRICH: Tangled Trig Graphs

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

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=sinx. 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=sin2x. 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

Age 16 to 18

Algebra & Pre-Algebra, Functions & Graphs, Trigonometry
High School, Educator

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