Question

question 16 (1 point)
the co - terminal angles to an angleθ may be determined using the expression
a) θ + 360°×n, n ∈ i
b) θ + 180°×n, n ∈ i
c) θ - 360°×n, n ∈ r
d) θ - 180°×n, n ∈ i

Explanation:

Co - terminal angles are angles that have the same terminal side. For an angle \(\theta\), adding or subtracting multiples of \(360^{\circ}\) (a full rotation) gives co - terminal angles. The general formula is \(\theta\pm360^{\circ}\times n\), where \(n\in I\) (the set of integers). Option a) \(\theta + 360^{\circ}\times n,n\in I\) is correct as it follows the formula for co - terminal angles. Option b) with \(180^{\circ}\) gives angles that are either supplementary or form a straight line - not co - terminal. Option c) has the wrong set (\(n\in\mathbb{R}\) is incorrect, it should be \(n\in I\)). Option d) also has \(180^{\circ}\) which is wrong for co - terminal angles.

Answer:

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