\begin{tabular}{l} HW Score: \( 68.75 \%, 11 \) of 16 points \\ \hline Give an expression that generates all angles coterminal with the given angle. \\ \( 30^{\circ} \)\end{tabular}

To find all angles coterminal with \( 30^{\circ} \), you can use the expression \( 30^{\circ} + 360^{\circ}k \), where \( k \) is any integer. This formula works because adding or subtracting full rotations (360 degrees) to any angle will yield an angle that lands in the same position on the unit circle. So, for instance, if \( k = 1 \), you'd get \( 390^{\circ} \), and if \( k = -1 \), it gives \( -330^{\circ} \). Keep in mind that coterminal angles can be positive or negative. If you want to generate a list, try substituting different integer values for \( k \). Negative values will lead to angles in the clockwise direction, while positive values will generate angles in the counterclockwise direction. This little trick will open a whole range of possible angles for you!