If `cos theta=(-5)/(12)`, in which quadrant does `theta` lie ?

Answer

To determine the quadrant in which the angle \( \theta \) lies given that \( \cos \theta = -\frac{5}{12} \), we can follow these steps:

### Step 1: Understand the Sign of Cosine
The cosine function is positive in the first and fourth quadrants and negative in the second and third quadrants. Since we are given that \( \cos \theta = -\frac{5}{12} \), this indicates that \( \theta \) must lie in either the second or third quadrant.

### Step 2: Identify the Quadrants
- **First Quadrant**: \( \cos \theta > 0 \)
- **Second Quadrant**: \( \cos \theta < 0 \)
- **Third Quadrant**: \( \cos \theta < 0 \)
- **Fourth Quadrant**: \( \cos \theta > 0 \)

Since \( \cos \theta \) is negative, we can eliminate the first and fourth quadrants.

### Step 3: Conclusion
Thus, \( \theta \) lies in either the second quadrant or the third quadrant.

### Final Answer
The angle \( \theta \) lies in the second or third quadrant.

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