4. For each of the following describe how the graph has changed from the standard 5 -point graph Write down the amplitude and equation of the axis for each. \( \begin{array}{lll}\text { a) } y=\sin \left(x+30^{\circ}\right) & \text { b) } y=5 \sin x & \text { c) } y=2 \sin \left(x-90^{\circ}\right)+1\end{array} \) \( 30^{\circ} \)

The first graph, \( y=\sin(x+30^{\circ}) \), introduces a horizontal shift or phase shift to the standard sine graph. It shifts to the left by \( 30^{\circ} \). The amplitude remains at 1, and the axis of the graph remains at \( y=0 \). In the second graph, \( y=5 \sin x \), we see an increase in amplitude, as the leading coefficient is 5, which stretches the graph vertically. The axis stays at \( y=0 \), but the peaks and troughs will now be at 5 and -5, respectively. For the third graph, \( y=2 \sin(x-90^{\circ}) + 1 \), there are two transformations: a horizontal shift to the right by \( 90^{\circ} \) and a vertical stretch due to the amplitude of 2. The vertical shift causes the axis to rise to \( y=1 \), and thus the new peaks will be at 3 and the troughs at -1.