https://file.aiquickdraw.com/mathbot/file/17274429419147ovgsjtf.jpg

Let's analyze the three trigonometric statements presented in the image:

### 1. **If \( \cos(x) = a \), then \( \cos(-x) = -a \):**
   - **False**: The cosine function is an **even function**, meaning \( \cos(-x) = \cos(x) \). Therefore, \( \cos(-x) \) equals \( a \), not \( -a \).

### 2. **If \( \sin(x) = a \), then \( \sin(-x) = -a \):**
   - **True**: The sine function is an **odd function**, meaning \( \sin(-x) = -\sin(x) \). So, if \( \sin(x) = a \), then \( \sin(-x) = -a \), making this statement true.

### 3. **If \( \tan(x) = a \), then \( \tan(-x) = -a \):**
   - **True**: The tangent function is also an **odd function**, meaning \( \tan(-x) = -\tan(x) \). Therefore, if \( \tan(x) = a \), then \( \tan(-x) = -a \), making this statement true as well.

### Conclusion:
- The correct true statements are:
  - Statement 2: \( \sin(x) = a \implies \sin(-x) = -a \)
  - Statement 3: \( \tan(x) = a \implies \tan(-x) = -a \)

Would you like further clarification on any of these points?

Here are 5 related questions:
1. What is the general difference between even and odd functions?
2. How do cosine, sine, and tangent functions behave under transformations like reflection?
3. What are the key properties of the sine function in terms of periodicity?
4. How can you derive trigonometric identities for negative angles?
5. Why do we refer to tangent as an odd function in trigonometry?

**Tip:** Understanding the symmetry of functions (even vs. odd) helps simplify many problems in trigonometry.

Which of the following statements are true? If cos(x) = a, then cos(-x) = -a; If sin(x) = a, then sin(-x) = -a; If tan(x) = a, then tan(-x) = -a.

Explore which trigonometric statements about cosine, sine, and tangent functions are true. Learn how to apply the properties of even and odd functions and understand key trigonometric identities for negative angles. Suitable for students in Grades 10-12.

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