Given the function:

\[
y = \sin(x) - 3
\]

To find the derivative \(\frac{dy}{dx}\), we'll differentiate each term with respect to \(x\).

1. The derivative of \(\sin(x)\) with respect to \(x\) is \(\cos(x)\).
2. The derivative of the constant \(-3\) is \(0\).

So, 

\[
\frac{dy}{dx} = \cos(x) + 0 = \cos(x)
\]

**Final answer:**

\[
\frac{dy}{dx} = \cos(x)
\]

Would you like further details or have any questions?

Here are some related questions to expand on this topic:

1. How do you differentiate other trigonometric functions like \(\cos(x)\) or \(\tan(x)\)?
2. What is the second derivative of \(y = \sin(x) - 3\)?
3. How do you find the derivative of \(\sin(x^2)\)?
4. What are the applications of derivatives in real-life scenarios?
5. How do you differentiate functions involving multiple trigonometric terms?

**Tip:** Always remember that the derivative of a constant is zero!

Learn how to find the derivative of y = sin(x) - 3 with a step-by-step solution. This problem involves key calculus concepts like differentiation and trigonometric functions, suitable for students in Grades 10-12.

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