Question Find the angle $\theta$ where $180^\circ \leq \theta \leq 360^\circ$ and $\cos \theta = \frac{\sqrt{2}}{2}$.

Studdy Solution
Since both $225^{\circ}$ and $315^{\circ}$ are within the interval $180^{\circ} \leq \theta \leq 360^{\circ}$, they are both valid solutions to the equation.
The solutions to the equation $\cos \theta = \frac{\sqrt{2}}{2}$ for $180^{\circ} \leq \theta \leq 360^{\circ}$ are $\theta = 225^{\circ}$ and $\theta = 315^{\circ}$.