Sine Function Ef6575

1. **State the problem:** We are given the function $$y=\sin x$$ and want to understand its properties. 2. **Formula and rules:** The sine function is a periodic trigonometric function defined as $$y=\sin x$$ where $$x$$ is an angle measured in radians. 3. **Key properties:** - The sine function oscillates between $$-1$$ and $$1$$. - It has zeros at $$x = n\pi$$ where $$n$$ is any integer. - The period of $$\sin x$$ is $$2\pi$$, meaning it repeats every $$2\pi$$ units. - The function is odd, so $$\sin(-x) = -\sin x$$. 4. **Graph features:** - Intercepts: at $$x=0, \pi, 2\pi, \ldots$$ - Extrema: maximum at $$x=\frac{\pi}{2} + 2n\pi$$ with value $$1$$, minimum at $$x=\frac{3\pi}{2} + 2n\pi$$ with value $$-1$$. This summarizes the function $$y=\sin x$$ and its main characteristics.