in what quadrant does the terminal side of angle θ lie if both the cosine and the tangent of θ are positive?

Answer 1

If both the cosine and the tangent of angle \( \theta \) are positive, then we can determine the quadrant in which the terminal side of the angle lies by analyzing the signs of the trigonometric functions.

1. Cosine Positive: The cosine of an angle is positive in the first and fourth quadrants.
2. Tangent Positive: The tangent of an angle is positive in the first and third quadrants.

Since \( \theta \) must satisfy both conditions (cosine positive and tangent positive), the only quadrant that meets these criteria is the first quadrant.

Therefore, the terminal side of angle \( \theta \) lies in the first quadrant.