To evaluate \(\cos(-810^\circ)\), we first reduce the angle to an equivalent angle between \(0^\circ\) and \(360^\circ\).

1. The cosine function is periodic with a period of \(360^\circ\). This means we can add or subtract multiples of \(360^\circ\) to simplify the angle:
   \[
   -810^\circ + 2(360^\circ) = -810^\circ + 720^\circ = -90^\circ
   \]
   So, \(\cos(-810^\circ) = \cos(-90^\circ)\).

2. We know that \(\cos(-90^\circ) = \cos(90^\circ)\), because cosine is an even function:
   \[
   \cos(-x) = \cos(x)
   \]
   Therefore, \(\cos(90^\circ) = 0\).

Thus, \(\cos(-810^\circ) = 0\).

Would you like more details on this process or have any other questions?

Here are some related questions:
1. What is \(\sin(-810^\circ)\)?
2. How do we calculate \(\cos(450^\circ)\)?
3. What is the period of the sine and cosine functions?
4. How does cosine's even property differ from sine's odd property?
5. How can you calculate \(\cos(-450^\circ)\) using a similar method?

**Tip:** For angles larger than \(360^\circ\) or negative angles, always use the periodic property of trigonometric functions to simplify them.

Learn how to calculate Cos(-810°) by reducing the angle using the periodic properties of cosine. Understand the concept of angle reduction and why Cos(-810°) equals Cos(90°), which is 0. This tutorial is suitable for students in Grades 10-12 studying trigonometry.

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