Question

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question 29 (1 point)
the co - terminal angles to an angle θ may be determined using the expression
a) θ - 180°×n,n ∈ i
b) θ + 180°×n,n ∈ i
c) θ + 360°×n,n ∈ i
d) θ - 360°×n,n ∈ r
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Explanation:

Coterminal angles are angles that share the same terminal side. By definition, to find coterminal angles to an angle \(\theta\), we add or subtract multiples of \(360^{\circ}\) (for angles measured in degrees). The general formula for coterminal angles is \(\theta\pm360^{\circ}\times n\), where \(n\in\mathbb{I}\) (the set of integers).

• Option a: \(\theta - 180^{\circ}\times n\) gives angles that are not coterminal in general. For example, if \(\theta = 30^{\circ}\) and \(n = 1\), we get \(- 150^{\circ}\), which is not coterminal with \(30^{\circ}\).
• Option b: \(\theta+180^{\circ}\times n\) gives angles that are not coterminal in general. For example, if \(\theta = 30^{\circ}\) and \(n = 1\), we get \(210^{\circ}\), which is not coterminal with \(30^{\circ}\).
• Option c: \(\theta + 360^{\circ}\times n\) (where \(n\in\mathbb{I}\)) is correct. If \(n = 0\), we have the angle \(\theta\) itself. If \(n=1\), \(\theta + 360^{\circ}\) is coterminal with \(\theta\), and if \(n=- 1\), \(\theta-360^{\circ}\) is coterminal with \(\theta\).
• Option d: \(n\in\mathbb{R}\) (the set of real numbers) is incorrect. The formula for coterminal angles uses integer multiples (\(n\in\mathbb{I}\)), not real - number multiples.

Answer:

C. \(\theta + 360^{\circ}\times n,n\in\mathbb{I}\)