To find the exact values of [tex]\( s \)[/tex] in the interval [tex]\([0, 2\pi)\)[/tex] that satisfy the condition [tex]\(\cos s = -\frac{\sqrt{3}}{2}\)[/tex], we need to identify the angles within this interval for which the cosine function equals [tex]\(-\frac{\sqrt{3}}{2}\)[/tex].
The cosine of an angle is [tex]\(-\frac{\sqrt{3}}{2}\)[/tex] at:
1. [tex]\( s = \frac{5\pi}{6} \)[/tex]
2. [tex]\( s = \frac{7\pi}{6} \)[/tex]
These angles are derived from the unit circle where the cosine values reach [tex]\(-\frac{\sqrt{3}}{2}\)[/tex]:
- At [tex]\( \frac{5\pi}{6} \)[/tex], which is in the second quadrant.
- At [tex]\( \frac{7\pi}{6} \)[/tex], which is in the third quadrant.
Thus, the exact values of [tex]\( s \)[/tex] in the interval [tex]\([0, 2\pi)\)[/tex] that satisfy the condition [tex]\(\cos s = -\frac{\sqrt{3}}{2}\)[/tex] are:
[tex]\[ s = \frac{5\pi}{6}, \frac{7\pi}{6} \][/tex]
So the final answer is:
[tex]\[ \frac{5\pi}{6}, \frac{7\pi}{6} \][/tex]
