Question

If $a=\sec {2000}^{\circ }$, then $a$ is

• A. $a>0$
• B. $a<0$
• C. $a=0$
• D. none of these

Answer 1

The correct option is B $a<0$

${2000}^{\circ }=5\times {360}^{\circ }+{200}^{\circ }$
$\therefore \sec {2000}^{\circ }=\sec (5\times {360}^{\circ }+{200}^{\circ })$
$=\sec {200}^{\circ }$
Since ${200}^{\circ }$ lies in third quadrant
$\therefore \sec {200}^{\circ }<0$