1. **State the problem:** We need to write an equation of the form $y = a \sin bx$ or $y = a \cos bx$ that describes the given graph. 2. **Analyze the graph:** The graph is a cosine wave with amplitude 1, period $2\pi$, and starts at $y=1$ when $x=0$. 3. **Recall the general form:** The general form for cosine is: $$y = a \cos bx$$ where $a$ is the amplitude and $b$ affects the period. 4. **Amplitude:** The amplitude $a$ is the maximum value of the wave, which is 1. 5. **Period:** The period $T$ of the function is related to $b$ by: $$T = \frac{2\pi}{b}$$ Given the wave completes one full cycle from $x=0$ to $x=2$, the period is $2$. 6. **Find $b$:** Using the period formula: $$2 = \frac{2\pi}{b} \implies b = \frac{2\pi}{2} = \pi$$ 7. **Write the equation:** Substitute $a=1$ and $b=\pi$ into the general form: $$y = 1 \cdot \cos(\pi x)$$ which simplifies to: $$y = \cos \pi x$$ **Final answer:** $$y = \cos \pi x$$