Question

which represents the measures of all angles coterminal with a 400° angle?
40 + 360n, for any whole number, n
360 + 40n, for any whole number, n
360 + 40n, for any integer, n
40 + 360n, for any integer, n

Explanation:

Step1: Find the reference angle

To find angles coterminal with \(400^{\circ}\), first find the reference angle. \(400 - 360=40^{\circ}\).

Step2: Use the coterminal - angle formula

The formula for coterminal angles is \(\theta=\alpha + 360n\), where \(\alpha\) is the reference angle and \(n\) is an integer. Here \(\alpha = 40^{\circ}\), so the formula becomes \(40+360n\) (\(n\in\mathbb{Z}\), \(n\) is an integer). Whole - number restriction is wrong because we can have negative coterminal angles (e.g., when \(n=- 1\), \(40-360=-320^{\circ}\) which is also coterminal with \(400^{\circ}\)).

Answer:

\(40 + 360n\), for any integer, \(n\) (the fourth option)