Solve for the angle , where 0 2
-$$\cos ^ { 2 } \theta = \frac { 3 } { 4 }$$
A) $\theta = \frac { \pi } { 3 } , \frac { 2 \pi } { 3 } , \frac { 4 \pi } { 3 } , \frac { 5 \pi } { 3 }$
B) $\theta = \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 4 }$
C) $\theta = \frac { \pi } { 6 } , \frac { 5 \pi } { 6 } , \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }$
D) $\theta = 0 , \pi , 2 \pi$

Question

Quizplus · Accepted Answer

We use the identity $\cos ^2 	heta = \frac{1+ \cos 2	heta}{2}$ to get $\frac{1+ \cos 2	heta}{2} = \frac34$. Solving this, we get $\cos 2	heta = \frac12$. Thus, $2	heta$ is equal to $\frac{\pi}{3}, \frac{5\pi}{3}$, so $	heta$ is equal to $\frac{\pi}{6}, \frac{5\pi}{6}$. Also, $2	heta$ is equal to $\frac{7\pi}{3}, \frac{11\pi}{3}$, so $	heta$ is equal to $\frac{7\pi}{6}, \frac{11\pi}{6}$. Therefore, the answer is $\boxed{	extbf{(C)} \: 	heta = \frac{\pi}{6}, \frac{5\pi}{6}, \frac{7\pi}{6}, \frac{11\pi}{6}}$.

Solve for the Angle , Where 0 2 - cos⁡2θ=34\cos ^ { 2 } \theta = \frac { 3 } { 4 }cos2θ=43​

Solve for the Angle , Where 0 2
- $\cos ^ { 2 } \theta = \frac { 3 } { 4 }$