### Degree Ceremony

What does Pythagoras' Theorem tell you about these angles: 90°, (45+x)° and (45-x)° in a triangle?

### Loch Ness

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

### Squareness

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?

# Tangled Trig Graphs

##### Stage: 5 Challenge Level:

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
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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