Find the exact values of s in the given interval that satisfy the given condition.
-$[ - \pi , \pi ) ; 2 \cos ^ { 2 } \mathrm {~s} = 1$

A) $\frac { \pi } { 4 } , \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 4 }$

B) $- \frac { 2 \pi } { 3 } , - \frac { \pi } { 3 } , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 }$

C) $- \frac { 7 \pi } { 4 } , - \frac { 5 \pi } { 4 } , - \frac { 3 \pi } { 4 } , - \frac { \pi } { 4 }$

D) $- \frac { 3 \pi } { 4 } , - \frac { \pi } { 4 } , \frac { \pi } { 4 } , \frac { 3 \pi } { 4 }$

Question

Find the exact values of s in the given interval that satisfy the given condition.
-$[ - \pi , \pi ) ; 2 \cos ^ { 2 } \mathrm {~s} = 1$

A) $\frac { \pi } { 4 } , \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 4 }$

B) $- \frac { 2 \pi } { 3 } , - \frac { \pi } { 3 } , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 }$

C) $- \frac { 7 \pi } { 4 } , - \frac { 5 \pi } { 4 } , - \frac { 3 \pi } { 4 } , - \frac { \pi } { 4 }$

D) $- \frac { 3 \pi } { 4 } , - \frac { \pi } { 4 } , \frac { \pi } { 4 } , \frac { 3 \pi } { 4 }$

Quizplus · Accepted Answer

The equation $2 \cos^2 s = 1$ simplifies to $\cos^2 s = \frac{1}{2}$. Taking the square root of both sides gives $\cos s = \pm \frac{\sqrt{2}}{2}$, which corresponds to the angles $\pm \frac{\pi}{4}$ and $\pm \frac{3\pi}{4}$ within the given interval $[- \pi , \pi )$.

Find the Exact Values of S in the Given Interval [−π,π);2cos⁡2 s=1[ - \pi , \pi ) ; 2 \cos ^ { 2 } \mathrm {~s} = 1[−π,π);2cos2 s=1

Find the Exact Values of S in the Given Interval $[ - \pi , \pi ) ; 2 \cos ^ { 2 } \mathrm {~s} = 1$