In which quadrant does the angle Θ lie given that
Cos Θ > 0 and tan Θ > 0?
A. Quadrant I
B. Quadrant II
C. Quadrant III
D. Quadrant IV
B?
All, Sin, Tan, Cos...ASTC
cos and tan are both >0 in quad I
Yes, you are correct. The angle Θ lies in Quadrant II. In this quadrant, both the cosine (Cos) and tangent (tan) are positive.
To determine the quadrant in which the angle Θ lies based on the given conditions, you can review the signs of the trigonometric functions in each quadrant. Here's how you can approach it:
1. Start with the given conditions: cos Θ > 0 and tan Θ > 0.
2. Recall that in the first quadrant (Quadrant I), all trigonometric functions are positive.
3. Determine the signs of cosine and tangent in the remaining quadrants:
- In Quadrant II, the cosine is negative, but the tangent is positive.
- In Quadrant III, both the cosine and tangent are negative.
- In Quadrant IV, the cosine is positive, but the tangent is negative.
4. Analyze the given conditions: cos Θ > 0 and tan Θ > 0.
- Since the cosine is positive (cos Θ > 0), it eliminates Quadrants III and IV, where the cosine is negative.
- Since the tangent is positive (tan Θ > 0), it eliminates Quadrants II and IV, where the tangent is negative.
5. By the process of elimination, you can conclude that the angle Θ lies in Quadrant I.
Therefore, the correct answer is A. Quadrant I.