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!