1. The problem asks why $\cos \theta$ is expressed as $\sqrt{1 - \sin^2 \theta}$. 2. This comes from the Pythagorean identity in trigonometry, which states: $$\sin^2 \theta + \cos^2 \theta = 1$$ 3. Rearranging this formula to solve for $\cos \theta$, we get: $$\cos^2 \theta = 1 - \sin^2 \theta$$ 4. To find $\cos \theta$, take the square root of both sides: $$\cos \theta = \pm \sqrt{1 - \sin^2 \theta}$$ 5. The $\pm$ indicates that cosine can be positive or negative depending on the quadrant of $\theta$. 6. In your problem, since $0 \leq \theta \leq \frac{\pi}{2}$ (first quadrant), cosine is positive, so: $$\cos \theta = \sqrt{1 - \sin^2 \theta}$$ 7. This explains why $\cos \theta$ is written as the square root of $1 - \sin^2 \theta$. Final answer: $$\cos \theta = \sqrt{1 - \sin^2 \theta}$$