Section 5.1: The Unit Circle

1. State the equation for the unit circle, and relate the equation to the distance formula we learned in Chapter 1.
2. Define the terminal point \((x, y)\) for a given real number \(t\).
3. Convert from an angle in radians to an angle in degrees and vice versa.
4. State the relationship between the distance traveled around the unit circle and the angle (in radians) traveled around the unit circle.
5. State the terminal points for \(t = k \cdot \frac{\pi}{6}\), \(t = k \cdot \frac{\pi}{4}\), \(t = k \cdot \frac{\pi}{3}\), and \(t = k \cdot \frac{\pi}{2}\) where \(k\) is a given integer.
6. Determine the reference number \(\bar{t}\) for a given real number \(t\).
7. Use the procedure in the grey box on page 406 of Stewart, Redlin, and Watson to find the terminal point for any real number \(t\) using \(t\)’s reference number \(\bar{t}\).

Section 5.2: Trigonometric Functions of Real Numbers

1. Relate the trigonmetric functions sine (\(\sin\)), cosine (\(\cos\)), tangent (\(\tan\)), secant (\(\sec\)), cosecant (\(\csc\)), and cotangent (\(\cot\)) to the terminal point associated with a real number \(t\).
2. Evaluate the trigonmetric functions above at \(t = k \cdot \frac{\pi}{6}\), \(t = k \cdot \frac{\pi}{4}\), \(t = k \cdot \frac{\pi}{3}\), and \(t = k \cdot \frac{\pi}{2}\) where \(k\) is a given integer.
3. Given a terminal point determined by a real number \(t\), determine the values of the trigonometric functions above evaluated at \(t\).
4. State the signs of sine, cosine, and tangent in each of the 4 quadrants of the coordinate plane.
5. Use the procedure in the grey box on page 412 of Stewart, Redlin, and Watson to evaluate the trigonometric functions at any real number.
6. State the Fundamental Identities given in the blue box of page 415 of Stewart, Redlin, and Watson.