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Degree Ceremony

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

After Thought

Which is larger cos(sin x) or sin(cos x) ? Does this depend on x ?


Sketch the graphs of y = sin x and y = tan x and some straight lines. Prove some inequalities.

Tangled Trig Graphs

Age 16 to 18 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