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# Can You Find... Trigonometry Edition

**This is an Underground Mathematics resource.**

*Underground Mathematics is hosted by Cambridge Mathematics. The project was originally funded by a grant from the UK Department for Education to provide free web-based resources that support the teaching and learning of post-16 mathematics.*

*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.*

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Age 16 to 18

Challenge Level

- Problem
- Student Solutions

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?