Question

Name the quadrant in which tan θ and sec θ are positive.

Answer 1

In the first quadrant, both tan θ and sec θ are positive.

Step-by-step explanation:

In the first quadrant, both $\tan\theta$ and $\sec\theta$ are positive.

This is because:

1. $\tan\theta$ is positive in the first and third quadrants. Since we are looking specifically for a positive value, we can conclude that $\tan\theta$ is positive in the first quadrant.
2. $\sec\theta$ is the reciprocal of $\cos\theta$. Since $\cos\theta$ is positive in the first quadrant (all $x$ values are positive), $\sec\theta$ is also positive in the first quadrant.