These are all graphs of sin. Some of which have some shifts to them. So you need to learn the ways to shift.
7. The first graph has no shift, so it is simply Sin(θ)
8. The graph actually has 2 transformations. The first is that it's magnitude goes up to 4. Also, you'll notice the peak starts t 0, which means that it moved back [tex] \frac{ \pi}{2} [/tex]. You can shift the magnitude by adding a number to the θ. So Sin(4θ) would take care of that. Then to move it backwards you subtract the number you move. So 8 should be Sin(4θ + [tex] \frac{ \pi}{2} [/tex])
If you Google Sin transformations you should find a number of helpful ways to remember these types of shifts.
