The sine of \(-120^\circ\) can be calculated as follows:

1. First, recognize that \(-120^\circ\) is in the third quadrant because it is between \(-180^\circ\) and \(-90^\circ\).
2. The reference angle for \(-120^\circ\) is \(180^\circ - 120^\circ = 60^\circ\).
3. In the third quadrant, the sine function is negative.

Thus:

\[
\sin(-120^\circ) = -\sin(60^\circ) = -\frac{\sqrt{3}}{2}
\]

So, \(\sin(-120^\circ) = -\frac{\sqrt{3}}{2}\).

Would you like more details or have any questions? Here are some related questions you might find interesting:

1. What is \(\sin(240^\circ)\)?
2. How do you find the cosine of \(-120^\circ\)?
3. What is the sine of \(-45^\circ\)?
4. What are the values of all trigonometric functions at \(-120^\circ\)?
5. How do you determine the quadrant of an angle given in degrees?

**Tip:** Remember that the sine of a negative angle is the negative sine of the corresponding positive angle due to the odd nature of the sine function.

Learn how to calculate sin(-120 degrees) using trigonometric principles. Understand why sin(-120 degrees) is equal to -sqrt(3)/2 and how angles are categorized in trigonometry. Suitable for high school students studying trigonometric functions.

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