Challenge Level

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?