In which quadrant does θ lie if the following statements are true: cosine, theta, is less than, 0, and , tangent, theta, is greater than, 0 cosθ<0 and tanθ>0
Based on the given statements, cosine of θ is less than 0 and tangent of θ is greater than 0.
In the unit circle, cosine is positive in the quadrants I and IV, and tangent is positive in quadrants I and III.
Since cosine is negative, it means that θ lies in either quadrant II or III.
Since tangent is positive, it means that θ lies in quadrant I.
Therefore, based on both conditions, θ lies in quadrant II.