4.1 Graphs of Sine and Cosine

Notes

The graphs of $y = \sin x$ and $y = \cos x$ are smooth waves that repeat every $2\pi$.

• Domain: all real numbers. Range: $[-1, 1]$. Period: $2\pi$.
• $y = \sin x$ starts at $(0, 0)$, rises to 1 at $\displaystyle \frac{\pi}{2}$, crosses zero at $\pi$, reaches $-1$ at $\displaystyle \frac{3\pi}{2}$, and returns to 0 at $2\pi$.
• $y = \cos x$ starts at $(0, 1)$, crosses zero at $\displaystyle \frac{\pi}{2}$, reaches $-1$ at $\pi$, crosses zero at $\displaystyle \frac{3\pi}{2}$, and returns to 1 at $2\pi$.
• Sine is odd (symmetric about the origin). Cosine is even (symmetric about the $y$-axis).