To find \(\cos(900^\circ)\), first, we reduce the angle using the periodicity of the cosine function. The cosine function has a period of \(360^\circ\), meaning it repeats every \(360^\circ\). So:

\[
900^\circ \mod 360^\circ = 900^\circ - 2 \times 360^\circ = 900^\circ - 720^\circ = 180^\circ
\]

Thus:

\[
\cos(900^\circ) = \cos(180^\circ)
\]

From trigonometric values, we know:

\[
\cos(180^\circ) = -1
\]

So, \(\cos(900^\circ) = -1\).

Would you like more details or have any questions?

Here are five related questions for practice:
1. What is \(\cos(540^\circ)\)?
2. How do you find \(\sin(450^\circ)\)?
3. What is the value of \(\tan(900^\circ)\)?
4. How does periodicity affect trigonometric functions?
5. Can you calculate \(\cos(1260^\circ)\)?

**Tip:** When dealing with large angles in trigonometry, always reduce them using the periodicity of \(360^\circ\) (for degrees) or \(2\pi\) (for radians).

Discover how to find the cosine of 900 degrees using trigonometric principles. This problem involves reducing large angles using the periodicity of cosine functions. Learn about angle reduction, trigonometric values, and more. Suitable for students and enthusiasts of trigonometry.

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