Find the reference angle for the angle \( 284^{\circ} \). The reference angle is (Type an integer or a decimai.)

To find the reference angle for \( 284^{\circ} \), you first determine which quadrant the angle lies in. Since \( 284^{\circ} \) is between \( 270^{\circ} \) and \( 360^{\circ} \), it's in the fourth quadrant. The reference angle can be calculated by subtracting \( 284^{\circ} \) from \( 360^{\circ} \): \[ 360^{\circ} - 284^{\circ} = 76^{\circ} \] So, the reference angle is \( 76^{\circ} \). To visualize this concept, think of a circle where each angle corresponds to a point along the perimeter. The reference angle is essentially how far the angle \( 284^{\circ} \) is from the nearest x-axis, helping to simplify calculations in trigonometry. This concept is crucial when working with sine, cosine, and tangent functions. When working with reference angles, a common mistake is to subtract the angle from \( 180^{\circ} \) instead of \( 360^{\circ} \) when dealing with angles in the fourth quadrant. Just remember, the correct formula for the fourth quadrant is always \( 360^{\circ} - \text{angle} \).