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Can You Find... Trigonometry Edition

Age 16 to 18 Challenge Level:

This resource is from Underground Mathematics.
 


Think of the types of graphs you can obtain by a combination of stretches, reflections and translations of the graph $y=\sin x$. In this resource we refer to any of these graphs as a "sine graph".

Can you find ...

(a) ... a sine graph which touches the lines $y=3$ and $y=1?$

(b) ... a cosine graph which crosses the $x$-axis at $x=1$ and $x=-1$?

(c) ... a tangent graph which passes through the point $\big(\dfrac{\pi}{3},0\big)$ and for which the line $x=\dfrac{\pi}{2}$ is an asymptote?

You can use the free Desmos graphing calculator to help you find suitable graphs, but try to sketch some graphs first.
Could you include extra conditions in parts (a), (b) or (c) so that the graphs are unique?


This is an Underground Mathematics resource.

Underground Mathematics is funded by a grant from the UK Department for Education and provides free web-based resources that support the teaching and learning of post-16 mathematics. It started in 2012 as the Cambridge Mathematics Education Project (CMEP).

Visit the site at undergroundmathematics.org to find more resources, which also offer suggestions, solutions and teacher notes to help with their use in the classroom.