Question

For what intervals of $x;$
$\sec x\text{is not greater than}0,\forall x\in (0,4\pi )?$

• A. $x\in (7\pi /2,4\pi )$
  
• B. $x\in (\pi /2,3\pi /2)$
• C. $x\in (3\pi /2,5\pi /2)$
• D. $x\in (0,\pi /2)$

Answer 1

The correct option is B $x\in (\pi /2,3\pi /2)$

For finding the region where $\sec x>0\forall x\in (0,4\pi ),$ for that let's draw the graph of $\sec x.$


Thus, from observing the graph, we can say $\sec x<0$ for
$x\in (\pi /2,3\pi /2)\cup (5\pi /2,7\pi /2)$
Hence the correct answer is Option (d).