Solve for x in the given interval.
-$$\sec x = - \frac { 2 \sqrt { 3 } } { 3 } , \frac { \pi } { 2 } \leq x \leq \pi$$
A) $\frac { 2 \pi } { 3 }$
B) $\frac { 3 \pi } { 4 }$
C) $\frac { 5 \pi } { 6 }$
D) $\frac { 7 \pi } { 6 }$

Question

Quizplus · Accepted Answer

The secant function is negative in the second quadrant. The given value $-\frac{2\sqrt{3}}{3}$ corresponds to $\sec x = \frac{1}{\cos x}$, where $\cos x = -\frac{\sqrt{3}}{2}$. In the interval $\frac{\pi}{2} \leq x \leq \pi$, this occurs at $x = \frac{5\pi}{6}$.

Solve for X in the Given Interval sec⁡x=−233,π2≤x≤π\sec x = - \frac { 2 \sqrt { 3 } } { 3 } , \frac { \pi } { 2 } \leq x \leq \pisecx=−323​​,2π​≤x≤π

Solve for X in the Given Interval $\sec x = - \frac { 2 \sqrt { 3 } } { 3 } , \frac { \pi } { 2 } \leq x \leq \pi$