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The problem asks you to simplify the expression "10 sin 45°" by first substituting the value of \( \sin 45^\circ \) and then simplifying the expression.

1. The value of \( \sin 45^\circ \) is \( \frac{\sqrt{2}}{2} \) or approximately 0.707.

2. Substitute this value into the expression:
   \[
   10 \cdot \sin 45^\circ = 10 \cdot \frac{\sqrt{2}}{2}
   \]

3. Simplify:
   \[
   10 \cdot \frac{\sqrt{2}}{2} = 5\sqrt{2} \quad \text{(exact form)}
   \]
   Or approximately:
   \[
   10 \cdot 0.707 = 7.07
   \]

So, the exact simplified expression is \( 5\sqrt{2} \), and the approximate numerical value is 7.07.

Would you like more details or have any other questions?

Here are some related questions to expand on this topic:
1. What is the definition of sine for angles on the unit circle?
2. How do you find the sine of other standard angles like 30° or 60°?
3. Why does \( \sin 45^\circ \) equal \( \frac{\sqrt{2}}{2} \)?
4. What other trigonometric functions can be evaluated at 45°?
5. How can you use the Pythagorean identity to check your sine values?

**Tip:** Memorizing the sine, cosine, and tangent of common angles like 0°, 30°, 45°, 60°, and 90° is helpful for quick calculations.

Simplify the expression by first substituting values from the table of exact values and then simplifying the resulting expression: 10 sin 45°.

Learn how to simplify the trigonometric expression 10 sin 45° using the exact value of sin 45°. This problem covers key trigonometric concepts and formulas. The exact result is 5√2, with an approximate numerical value of 7.07. Suitable for Grades 9-10 students studying trigonometry.

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