In which quadrant does $\theta$ lie if the following statements are true:
\[
\cos \theta> 0 \text { and } \tan \theta< 0
\]

Answer

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Answer

$\theta$ lies in the $\boxed{fourth}$ quadrant.

Steps

Step 1 ：The cosine function is positive in the first and fourth quadrants.

Step 2 ：The tangent function is negative in the second and fourth quadrants.

Step 3 ：Therefore, if both conditions are true, $\theta$ must lie in the fourth quadrant.

Step 4 ：$\theta$ lies in the $\boxed{fourth}$ quadrant.