Find the exact values of s in the given interval that satisfy the given condition.
-$$[ - 2 \pi , \pi ) ; \cos ^ { 2 } \mathrm {~s} = \frac { 3 } { 4 }$$
A) $- \frac { 5 \pi } { 3 } , - \frac { \pi } { 3 } , \frac { \pi } { 3 }$
B) $- \frac { 5 \pi } { 3 } , - \frac { 4 \pi } { 3 } , - \frac { 2 \pi } { 3 } , - \frac { \pi } { 3 } , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 }$
C) $- \frac { 11 \pi } { 6 } , - \frac { 7 \pi } { 6 } , - \frac { 5 \pi } { 6 } , - \frac { \pi } { 6 } , \frac { \pi } { 6 } , \frac { 5 \pi } { 6 }$
D) $- \frac { 11 \pi } { 6 } , - \frac { \pi } { 6 } , \frac { \pi } { 6 }$

Question

Quizplus · Accepted Answer

Given $\cos^2 s = \frac{3}{4}$, we find $\cos s = \pm \sqrt{\frac{3}{4}} = \pm \frac{\sqrt{3}}{2}$. The values of $s$ in the interval $[-2\pi, \pi)$ that satisfy this are $-\frac{11\pi}{6}, -\frac{7\pi}{6}, -\frac{5\pi}{6}, -\frac{\pi}{6}, \frac{\pi}{6}, \frac{5\pi}{6}$, corresponding to the angles where the cosine function equals $\pm \frac{\sqrt{3}}{2}$.

Find the Exact Values of S in the Given Interval [−2π,π);cos⁡2 s=34[ - 2 \pi , \pi ) ; \cos ^ { 2 } \mathrm {~s} = \frac { 3 } { 4 }[−2π,π);cos2 s=43​

Find the Exact Values of S in the Given Interval $[ - 2 \pi , \pi ) ; \cos ^ { 2 } \mathrm {~s} = \frac { 3 } { 4 }$