The exact value of \(\sin(-240^\circ)\) can be found as follows:

1. **Determine the reference angle**: 
   - Since \(-240^\circ\) is a negative angle, we first find its positive equivalent by adding \(360^\circ\).
   - \(-240^\circ + 360^\circ = 120^\circ\).

   So, the reference angle is \(120^\circ\).

2. **Identify the sine of the reference angle**:
   - The sine of \(120^\circ\) is equivalent to the sine of its reference angle in the first quadrant, which is \(60^\circ\).
   - \(\sin(120^\circ) = \sin(60^\circ) = \frac{\sqrt{3}}{2}\).

3. **Determine the sign based on the quadrant**:
   - The angle \(120^\circ\) is in the second quadrant, where sine is positive.
   - However, \(-240^\circ\) corresponds to the same position but is in the third quadrant, where sine is negative.

Thus, \(\sin(-240^\circ) = -\sin(120^\circ) = -\frac{\sqrt{3}}{2}\).

### Answer:
The exact value of \(\sin(-240^\circ)\) is \(-\frac{\sqrt{3}}{2}\).

Would you like a detailed explanation on a particular step, or have any further questions?

---

1. What is the sine of \(240^\circ\)?
2. How do you find the reference angle for any angle?
3. Why is the sine function negative in the third quadrant?
4. How does the sine function behave with negative angles?
5. What are the exact trigonometric values of commonly known angles?

**Tip**: Always check the quadrant of your angle to determine the sign of the trigonometric function.

Learn how to find the exact value of sin(-240°) using trigonometric principles. This problem covers trigonometric values, reference angles, and quadrant analysis. Suitable for high school students studying trigonometry.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation