Find the exact value of the trigonometric function. (If an answer is undefined, enter UNDEFINED.)

sin(240°)

To find the exact value of \( \sin(240^\circ) \), follow these steps:

1. **Determine the reference angle:**
   - \( 240^\circ \) is in the third quadrant, where sine is negative.
   - The reference angle is \( 240^\circ - 180^\circ = 60^\circ \).

2. **Use the sine value of the reference angle:**
   - \( \sin(60^\circ) = \frac{\sqrt{3}}{2} \).

3. **Adjust for the sign in the third quadrant:**
   - In the third quadrant, sine is negative.
   - Thus, \( \sin(240^\circ) = -\frac{\sqrt{3}}{2} \).

So, the exact value of \( \sin(240^\circ) \) is:
\[
\sin(240^\circ) = -\frac{\sqrt{3}}{2}
\]

Would you like any additional details or have any questions?

---

Here are 5 related questions:
1. What is the cosine of \( 240^\circ \)?
2. How do you find the reference angle for \( 300^\circ \)?
3. What is the exact value of \( \sin(120^\circ) \)?
4. Why is sine negative in the third quadrant?
5. How does the unit circle help in finding trigonometric values?

**Tip:** Memorizing the sine and cosine values for common angles (30°, 45°, 60°) can greatly speed up solving trigonometric problems.

Find the exact value of the trigonometric function. (If an answer is undefined, enter UNDEFINED.) sin(240°)

Learn how to find the exact value of sin(240°) using reference angles and trigonometric principles. This problem explores key trigonometry concepts like reference angles, the sine function's sign in different quadrants, and the unit circle. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation