The value of ` tan (-945^(@))` is

Options

A. `-1`
B. `-2`
C. `-3`
D. `-4`

Answer

To find the value of \( \tan(-945^\circ) \), we can follow these steps:

### Step-by-Step Solution:

1. **Use the property of tangent for negative angles**:
\[ \tan(-\theta) = -\tan(\theta) \]
Applying this to our problem:
\[ \tan(-945^\circ) = -\tan(945^\circ) \]

2. **Reduce the angle**:
To simplify \( \tan(945^\circ) \), we can reduce it by subtracting multiples of \( 360^\circ \) (since the tangent function has a period of \( 360^\circ \)):
\[ 945^\circ - 2 \times 360^\circ = 945^\circ - 720^\circ = 225^\circ \]
Thus, we have:
\[ \tan(945^\circ) = \tan(225^\circ) \]

3. **Find the value of \( \tan(225^\circ) \)**:
The angle \( 225^\circ \) is in the third quadrant, where the tangent function is positive. The reference angle for \( 225^\circ \) is \( 225^\circ - 180^\circ = 45^\circ \). Therefore:
\[ \tan(225^\circ) = \tan(45^\circ) = 1 \]

4. **Combine the results**:
Now substituting back:
\[ \tan(-945^\circ) = -\tan(945^\circ) = -\tan(225^\circ) = -1 \]

### Final Answer:
\[ \tan(-945^\circ) = -1 \]

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