To find \(\sin(900^\circ)\), we use the periodicity of the sine function, which also repeats every \(360^\circ\).

First, reduce the angle:

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

So:

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

From trigonometric values, we know:

\[
\sin(180^\circ) = 0
\]

Therefore, \(\sin(900^\circ) = 0\).

Would you like more details or have any questions?

Here are five related questions for practice:
1. What is \(\sin(450^\circ)\)?
2. How do you calculate \(\cos(900^\circ)\)?
3. What is the value of \(\tan(900^\circ)\)?
4. How does the sine function behave at angles like \(540^\circ\) or \(720^\circ\)?
5. Can you find \(\sin(1260^\circ)\)?

**Tip:** Always simplify angles using modulo \(360^\circ\) when working with sine or cosine in degrees.

Learn how to calculate sin(900 degrees) using trigonometric values and periodicity of sine function. Explore step-by-step solution with key formulas and theorems applied. Suitable for high school students.

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