Use a unit circle diagram to find the values of cos(-270°) and sin(-270°).

To find the values of \( \cos(-270^\circ) \) and \( \sin(-270^\circ) \), we use the unit circle.

### Steps:

1. **Understanding the negative angle**: 
   - A negative angle means we move clockwise around the unit circle.
   - Starting at \( 0^\circ \) (positive x-axis), move \( 270^\circ \) clockwise.

2. **Locate the angle**:
   - Moving \( 270^\circ \) clockwise from \( 0^\circ \), we land at the \( 90^\circ \) position in the **positive y-axis direction**. This is equivalent to \( -270^\circ \).

3. **Coordinates on the unit circle**:
   - The coordinates of the point at \( 90^\circ \) (or \( -270^\circ \)) are \( (0, 1) \), where:
     - \( x = \cos(\text{angle}) \)
     - \( y = \sin(\text{angle}) \)

4. **Values**:
   - \( \cos(-270^\circ) = x = 0 \)
   - \( \sin(-270^\circ) = y = 1 \)

### Final Answer:
\[
\cos(-270^\circ) = 0
\]
\[
\sin(-270^\circ) = 1
\]

Would you like me to illustrate the unit circle diagram or explain further? Here are some related questions:

1. How do you calculate trigonometric functions for angles greater than \( 360^\circ \)?
2. What are the coordinates for common angles like \( 30^\circ, 45^\circ, \text{and } 60^\circ \)?
3. How does symmetry on the unit circle help with trigonometric calculations?
4. Can you explain how reference angles work on the unit circle?
5. Why do \( \cos \) and \( \sin \) repeat their values every \( 360^\circ \)?

**Tip**: When working with negative angles, always visualize them as moving clockwise around the unit circle!

Learn how to determine the values of cos(-270°) and sin(-270°) using a unit circle diagram. This step-by-step guide explains trigonometric functions for negative angles and provides insight into unit circle properties. Ideal for Grades 10-12 students.

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