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Degree Ceremony

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

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Loch Ness

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

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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: Challenge Level:1
This anonymous solver correctly identified the remaining curves, and explained how to draw a graph of sin $x$ using the cosine function:

The red graph has equation $y=-\sin x$.
The light blue graph has equation $y=\sin 2x$.
The grey graph has equation $y=\sin 3x$.
The dark blue graph has equation $y=-\sin 3x$.

The graph $y=\cos x$ is the same shape as $y=\sin x$ but shifted along. I can make the shape of $y=\sin x$ by drawing the graph $y=\cos (x-90^{\circ})$


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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