1. **State the problem:** We have the curve given by the function $$y=\frac{\cos x}{2-\sin x}$$ and need to find the coordinates of points A and C where the curve intersects the x-axis and y-axis respectively. 2. **Find point A (x-intercept):** The curve intersects the x-axis where $$y=0$$. Set $$\frac{\cos x}{2-\sin x} = 0$$. Since the denominator cannot be zero (to avoid division by zero), the numerator must be zero: $$\cos x = 0$$ 3. **Solve for x:** $$\cos x = 0 \implies x = \frac{\pi}{2} + k\pi, \quad k \in \mathbb{Z}$$ 4. **Find corresponding y-coordinate:** At these x-values, $$y=0$$ by definition of x-intercept. So the x-intercepts are at points: $$A_k = \left(\frac{\pi}{2} + k\pi, 0\right)$$ 5. **Find point C (y-intercept):** The curve intersects the y-axis where $$x=0$$. Evaluate $$y$$ at $$x=0$$: $$y = \frac{\cos 0}{2 - \sin 0} = \frac{1}{2 - 0} = \frac{1}{2}$$ So the y-intercept is: $$C = (0, \frac{1}{2})$$ **Final answers:** $$A_k = \left(\frac{\pi}{2} + k\pi, 0\right), \quad k \in \mathbb{Z}$$ $$C = \left(0, \frac{1}{2}\right)$$