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

What are you looking for?

Organization

NRICH (University of Cambridge)

Website URL

Type of Resource

Challenge

Assigned Categories