The expression \( \sin(-x) + \sin(x) \) can be evaluated using the properties of the sine function.

1. **Using the Odd Function Property of Sine:** 
   Sine is an odd function, meaning \( \sin(-x) = -\sin(x) \).

2. **Substitute \( \sin(-x) = -\sin(x) \):**
   \[
   \sin(-x) + \sin(x) = -\sin(x) + \sin(x)
   \]

3. **Simplify the Expression:**
   \[
   -\sin(x) + \sin(x) = 0
   \]

### Final Answer:
\[
\sin(-x) + \sin(x) = 0
\]

Would you like further explanation, or do you have any questions?

Here are some related questions that might deepen your understanding:

1. What are other examples of trigonometric identities that involve odd and even functions?
2. How does the property of odd functions affect other trigonometric functions?
3. What is the result of \( \cos(-x) + \cos(x) \)?
4. How would you handle \( \tan(-x) + \tan(x) \)?
5. Can you apply similar properties for other functions like exponential or logarithmic?

**Tip:** Remember that even functions, like \( \cos(x) \), satisfy \( f(-x) = f(x) \), while odd functions, like \( \sin(x) \), satisfy \( f(-x) = -f(x) \).

Explore the solution to sin(-x) + sin(x) by applying trigonometric properties. This problem demonstrates the odd function property of sine, simplifying the expression to zero. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation