Plotting a graph takes time. Often mathematicians just want to know the key features. These are: shape, location and some key points (such as where the graph crosses the axes or turning points).

In a function such as sine or cosine, we could also have a translation of the form: \(y = \sin (x - a)^\circ\) where \(a\) is called the phase angle. This is when the graph of the function has been ...