The function given is:
$f(x) = \sin x$ This is the sine function, a fundamental trigonometric function. Here are some key properties:

1. Domain: $(-\infty, \infty)$ (all real numbers)
2. Range: $[-1, 1]$
3. Periodicity: The function is periodic with period $2\pi$, meaning $\sin(x + 2\pi) = \sin x$.
4. Symmetry: It is an odd function, satisfying $\sin(-x) = -\sin x$, which means it is symmetric about the origin.
5. Derivatives:
   • First derivative: $f'(x) = \cos x$
   • Second derivative: $f''(x) = -\sin x$

Would you like more details or have any questions?

Related Questions:

1. What is the graph of $f(x) = \sin x$ and how does it behave?
2. How do we calculate the Fourier series for $f(x) = \sin x$?
3. What happens when we apply transformations like shifting or scaling to $f(x)$?
4. How is $\sin x$ used in physics and engineering?
5. How does the Taylor series expansion of $\sin x$ work?

Tip:

The sine function is widely used in oscillations, waves, and circular motion. Understanding its derivatives and transformations can help in solving real-world problems!