Section 5.3: Trigonometric Graphs

1. Relate the graphs of \(\sin t\) and \(\cos t\) to the terminal point \((x, y)\) a distance \(t\) from the point \((1, 0)\) along the unit circle.
2. State what property a function must have to be periodic.
3. State the period of \(\sin t\) and \(\cos t\).
4. Sketch one period of the graphs of \(\sin t\) and \(\cos t\).
5. Identify the amplitude and period of the functions \(s(t) = a \sin k(t - h)\) and \(c(t) = a \cos k(t - h)\).
6. Explain the impacts of \(a\), \(k\), \(v\), and \(h\) on the transformations \(s(t) = v + a \sin k(t - h)\) and \(c(t) = v + a \cos k(t - h)\) of \(\sin t\) and \(\cos t\), and how they impact the graphs of the transformations.
7. Identify the functions \(s(t) = v + a \sin k(t - h)\) and \(c(t) = v + a \cos k(t - h)\) from a graph of a single period.
8. Identify the domain and range of the functions \(\sin t\), \(\cos t\), \(s(t) = v + a \sin k(t - h)\), and \(c(t) = v + a \cos k(t - h)\).

Section 5.4: More Trigonometric Graphs

1. State the period of \(\tan t\), \(\cot t\), \(\sec t\), and \(\csc t\).
2. Sketch one period of \(\tan t\), \(\cot t\), \(\sec t\), and \(\csc t\).t