Given sin x =5/2 find the exact value of sin 2x

Given that \( \sin x = \frac{5}{2} \), this value is not valid because the sine function's range is limited to \( -1 \leq \sin x \leq 1 \). Since \( \frac{5}{2} = 2.5 \) is outside this range, it is impossible for \( \sin x \) to equal \( \frac{5}{2} \).

Could you double-check the value you provided for \( \sin x \)? It might be a typo or mistake. Feel free to provide the correct value, and I can help you find \( \sin 2x \).

Would you like to proceed with another question or clarification? Here are five questions that can extend this topic:

1. How do we find the double-angle identity for sine?
2. What happens if \( \sin x \) is larger than 1?
3. How do you calculate \( \sin 2x \) using trigonometric identities?
4. What are the implications if \( \sin x = \frac{5}{2} \) in a theoretical context?
5. Can the sine function have any other range in a different mathematical system?

**Tip**: The double-angle identity for sine is \( \sin 2x = 2 \sin x \cos x \).

Given sin x = 5/2 find the exact value of sin 2x

Explore why sin x = 5/2 is not valid in trigonometry and how to use the double-angle identity sin 2x = 2 sin x cos x for valid sine values. This problem focuses on the range of the sine function and trigonometric identities. Suitable for students in Grades 9-12.

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