Can you find... trigonometry edition

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Can you find …

1. … two sine graphs which only cross each other on the \(x\)-axis?

2. … a sine graph, a cosine graph and a tangent graph which all meet at certain points? What if all three graphs have to meet at the origin?

3. … a sine graph and a cosine graph which don’t cross each other? What if the graphs have to lie between \(y=1\) and \(y=-1\)?

4. … a cosine graph and a tangent graph which meet the \(x\)-axis the same number of times between \(x=-4\) and \(x=4\)? What if these points have to be the same for both graphs?

Note that by “a sine graph” we mean any curve which is obtained by some combination of stretches, reflections and translations of the graph \(y=\sin x\).

You can use Desmos to help you find suitable graphs, but try to sketch some graphs first.