Find all angles, \( 0^{\circ} \leq \theta<360^{\circ} \), that solve the following equation. \[ \cos \theta=\frac{\sqrt{3}}{2} \]

The equation to solve is \[ \cos \theta = \frac{\sqrt{3}}{2}. \] This equation asks for the angle(s) \(\theta\) within the interval \(0^{\circ} \leq \theta < 360^{\circ}\) for which the cosine value is \(\frac{\sqrt{3}}{2}\). ### Step 1. Identify the reference angle We know that \[ \cos 30^{\circ} = \frac{\sqrt{3}}{2}. \] Thus, the reference angle is \(30^{\circ}\). ### Step 2. Determine in which quadrants \(\cos \theta\) is positive Cosine is positive in the first quadrant and the fourth quadrant. - **First Quadrant:** The angle itself is \(30^{\circ}\). - **Fourth Quadrant:** The angle is given by \(360^{\circ} - 30^{\circ} = 330^{\circ}\). ### Step 3. Write the solution The angles in the interval \(0^{\circ} \leq \theta < 360^{\circ}\) that satisfy the equation are: \[ \theta = 30^{\circ} \quad \text{and} \quad \theta = 330^{\circ}. \]