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The moudel is Angles on the Unit Circle

what's the answear

The problem asks for the value of \( \sin(330^\circ) \), and the provided diagram shows a unit circle with a 30° reference angle in the fourth quadrant.

### Step-by-Step Solution:
1. **Identify the Reference Angle**:  
   The angle \( 330^\circ \) is in the fourth quadrant. The reference angle for \( 330^\circ \) is:
   \[
   360^\circ - 330^\circ = 30^\circ
   \]
   
2. **Use the Sine of the Reference Angle**:  
   For a reference angle of \( 30^\circ \), the sine value is known to be:
   \[
   \sin(30^\circ) = \frac{1}{2}
   \]
   
3. **Determine the Sign**:  
   In the fourth quadrant, the sine function is negative (since the y-coordinate is negative on the unit circle). Therefore:
   \[
   \sin(330^\circ) = -\sin(30^\circ) = -\frac{1}{2}
   \]

### Final Answer:
\[
\sin(330^\circ) = -\frac{1}{2}
\]

Would you like further details on the unit circle, or do you have any questions?

### Related Questions:
1. What is the value of \( \cos(330^\circ) \)?
2. How do you determine the reference angle for any given angle?
3. What is the value of \( \sin(210^\circ) \)?
4. Why is the sine negative in the fourth quadrant?
5. How is the unit circle used to find trigonometric functions?

**Tip**: Remember that the signs of trigonometric functions depend on the quadrant of the angle.

Learn how to find the value of sin(330°) using the unit circle and the reference angle of 30°. This trigonometry problem involves understanding quadrant signs and applying known trigonometric values. Suitable for students in Grades 9-12.

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