Math Problem Statement

sin(-x)+sin(x)=?

Solution

The expression sin(x)+sin(x)\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)\sin(-x) = -\sin(x).

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

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

Final Answer:

sin(x)+sin(x)=0\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)\cos(-x) + \cos(x)?
  4. How would you handle tan(x)+tan(x)\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)\cos(x), satisfy f(x)=f(x)f(-x) = f(x), while odd functions, like sin(x)\sin(x), satisfy f(x)=f(x)f(-x) = -f(x).

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Odd and Even Functions

Formulas

sin(-x) = -sin(x)

Theorems

Odd Function Property of Sine

Suitable Grade Level

Grades 10-12