Give an expression that generates all angles coterminal with the given angle.
\[
30^{\circ}
\]

Step 1 ：Coterminal angles are angles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side. For example 30°, 390° and -330° are all coterminal because they end at the same position on the circle, despite having different amounts of rotation.

Step 2 ：To generate all angles coterminal with a given angle, we can add or subtract multiples of 360° (a full rotation) to the given angle.

Step 3 ：So, the expression to generate all angles coterminal with a given angle \(θ\) is: \[θ + 360n\] where \(n\) is an integer.

Step 4 ：Applying this to the given angle of 30°, we get the expression \[30 + 360n\].

Step 5 ：Using this expression, we can generate all angles coterminal with 30° by substituting different integer values for \(n\).

Step 6 ：For example, the coterminal angles within the range of \(n = -10\) to \(n = 10\) are \[-3570, -3210, -2850, -2490, -2130, -1770, -1410, -1050, -690, -330, 30, 390, 750, 1110, 1470, 1830, 2190, 2550, 2910, 3270, 3630\].

Step 7 ：\[\boxed{\text{Final Answer: The expression that generates all angles coterminal with the given angle } 30^\circ \text{ is } 30 + 360n, \text{ where } n \text{ is an integer. The coterminal angles within the range of } n = -10 \text{ to } n = 10 \text{ are } [-3570, -3210, -2850, -2490, -2130, -1770, -1410, -1050, -690, -330, 30, 390, 750, 1110, 1470, 1830, 2190, 2550, 2910, 3270, 3630].}\]