Question

Solve for x in the given interval. sec x= -2√3/3, for π/2 ≤x≤π

Answer 1

Answer:

b. $x=\frac{5\pi}{6}$

Step-by-step explanation:

The given function is

$\sec x=-\frac{2\sqrt{3} }{3},\:\:for\:\:\frac{\pi}{2}\le x \le \pi$

Recall that the reciprocal of the cosine ratio is the secant ratio.

This implies that;

$\frac{1}{\cos x}=-\frac{2\sqrt{3} }{3}$

$\Rightarrow \cos x=-\frac{3}{2\sqrt{3} }$

$\Rightarrow \cos x=-\frac{\sqrt{3}}{2}$

We take the inverse cosine of both sides to obtain;

$x=\cos^{-1}(-\frac{\sqrt{3}}{2})$

$x=\frac{5\pi}{6}$