https://file.aiquickdraw.com/mathbot/file/1728436206235coin6rxy.jpg

Let's solve the questions from the image you provided. We are given three trigonometric identities and need to find the corresponding negative angle values.

### 1. \(\tan(x) = -0.5\), then \(\tan(-x)\)
Using the odd function property of the tangent function:
\[
\tan(-x) = -\tan(x)
\]
So,
\[
\tan(-x) = -(-0.5) = 0.5
\]

### 2. \(\sin(x) = 0.8\), then \(\sin(-x)\)
The sine function is odd, meaning:
\[
\sin(-x) = -\sin(x)
\]
So,
\[
\sin(-x) = -0.8
\]

### 3. \(\cos(x) = 0.7\), then \(\cos(-x)\)
The cosine function is even, meaning:
\[
\cos(-x) = \cos(x)
\]
So,
\[
\cos(-x) = 0.7
\]

### Final answers:
1. \(\tan(-x) = 0.5\)
2. \(\sin(-x) = -0.8\)
3. \(\cos(-x) = 0.7\)

Would you like more details or have any questions? Here are some related questions you might find helpful:

1. What are the properties of odd and even trigonometric functions?
2. How do negative angles affect the values of other trigonometric functions?
3. What happens to trigonometric values when angles exceed \(360^\circ\)?
4. Can these principles be applied to radians as well as degrees?
5. How does the unit circle relate to the signs of trigonometric functions?

**Tip:** Remember that odd functions (like sine and tangent) change signs when evaluated at negative angles, while even functions (like cosine) remain unchanged!

If tan(x) = -0.5, sin(x) = 0.8, and cos(x) = 0.7, find tan(-x), sin(-x), and cos(-x).

Learn how to solve for tan(-x), sin(-x), and cos(-x) given tan(x) = -0.5, sin(x) = 0.8, and cos(x) = 0.7 using properties of odd and even functions in trigonometry. This problem is suitable for high school students in Grades 9-12.

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