Decide whether the expression is or is not an identity.
-Find $\cos \frac { \theta } { 2 }$, given that $\sin \theta = \frac { 1 } { 4 }$ and $\theta$ terminates in $0

Question

Decide whether the expression is or is not an identity.
-Find $\cos \frac { \theta } { 2 }$, given that $\sin \theta = \frac { 1 } { 4 }$ and $\theta$ terminates in $0 < \theta < 90 ^ { \circ }$.
A) $\frac { \sqrt { 10 } } { 4 }$
B) $\frac { \sqrt { 8 + 2 \sqrt { 15 } } } { 4 }$
C) $\frac { \sqrt { 6 } } { 4 }$
D) $\frac { \sqrt { 8 - 2 \sqrt { 15 } } } { 4 }$

Quizplus · Accepted Answer

Using the half-angle identity $\cos \frac{\theta}{2} = \sqrt{\frac{1 + \cos \theta}{2}}$ and $\cos \theta = \sqrt{1 - \sin^2 \theta} = \sqrt{\frac{15}{16}}$, we find $\cos \frac{\theta}{2} = \frac{\sqrt{8 + 2\sqrt{15}}}{4}$.

Decide Whether the Expression Is or Is Not an Identity cos⁡θ2\cos \frac { \theta } { 2 }cos2θ​

Decide Whether the Expression Is or Is Not an Identity $\cos \frac { \theta } { 2 }$