QuestionQuestion 4 (2 points) Solve the following equation for $0 \leq \theta \leq 2 \pi$. Select all correct solutions. $$\sec \theta-\sqrt{2}=0$$
Select 2 correct answer(s)

Studdy Solution
Find the values of $\theta$ that satisfy $\cos \theta = \frac{\sqrt{2}}{2}$ within the interval $0 \leq \theta \leq 2\pi$. These values are known from the unit circle:
$\theta = \frac{\pi}{4}, \quad \theta = \frac{7\pi}{4}$
These are the angles where the cosine value is $\frac{\sqrt{2}}{2}$.
The correct solutions for $\theta$ are:
$\boxed{\frac{\pi}{4}} \quad \text{and} \quad \boxed{\frac{7\pi}{4}}$