Question

give an expression that generates all angles coterminal with the given angle.
360°
the correct expression is 360° + □°.
(type an expression using n as the variable.)

Explanation:

Step1: Recall coterminal angle formula

Coterminal angles are found by adding or subtracting multiples of \(360^\circ\) (for degrees) to the given angle. The general formula for coterminal angles with an angle \(\theta\) in degrees is \(\theta + n\cdot360^\circ\), where \(n\) is any integer (positive, negative, or zero).

Step2: Apply formula to given angle

The given angle is \(360^\circ\). Using the coterminal angle formula, we substitute \(\theta = 360^\circ\). So the expression for all coterminal angles is \(360^\circ + n\cdot360^\circ\)? Wait, no, wait. Wait, actually, let's re - examine. Wait, the problem says "The correct expression is \(360^\circ+\square^\circ\)". Wait, maybe there's a mis - reading. Wait, no, the given angle is \(360^\circ\). The formula for coterminal angles is \(\theta + n\times360^\circ\), where \(n\in\mathbb{Z}\). But if the template is \(360^\circ+\square^\circ\), then we need to express it as \(360^\circ + n\times360^\circ\)? Wait, no, that can't be. Wait, maybe the given angle is \(0^\circ\) (since \(360^\circ\) is coterminal with \(0^\circ\))? Wait, no, the problem says the given angle is \(360^\circ\). Wait, let's think again. The general formula for coterminal angles with an angle \(\alpha\) is \(\alpha + n\cdot360^\circ\), \(n\in\mathbb{Z}\). So for \(\alpha = 360^\circ\), the coterminal angles are \(360^\circ+n\cdot360^\circ\). But the problem's template is \(360^\circ+\square^\circ\). Wait, maybe there's a typo, but assuming that we need to put \(n\times360\) in the square? Wait, no, the problem says "Type an expression using \(n\) as the variable". So the expression should be \(360^\circ + n\cdot360^\circ\)? But the template is \(360^\circ+\square^\circ\), so the square should be \(360n\). Because \(360^\circ + 360n^\circ\) (where \(n\) is an integer) gives all coterminal angles with \(360^\circ\) (since adding or subtracting multiples of \(360^\circ\) to \(360^\circ\) will give angles like \(360^\circ+360^\circ = 720^\circ\), \(360^\circ - 360^\circ=0^\circ\), etc., which are coterminal with \(360^\circ\)).

Answer:

\(360n\) (so the expression is \(360^{\circ}+360n^{\circ}\), and the value in the square is \(360n\))