Use The Half-Angle Formulas
-$\sin \frac { 3 \pi } { 8 }$
A) $\frac { 1 } { 2 } \sqrt { 2 + \sqrt { 2 } }$
B) $\frac { 1 } { 2 } \sqrt { 2 - \sqrt { 2 } }$
C) $- \frac { 1 } { 2 } \sqrt { 2 + \sqrt { 2 } }$
D) $- \frac { 1 } { 2 } \sqrt { 2 - \sqrt { 2 } }$

Question

Quizplus · Accepted Answer

The half-angle formula for sine is $\sin \frac{\theta}{2} = \pm \sqrt{\frac{1 - \cos \theta}{2}}$. To find $\sin \frac{3\pi}{8}$, we first recognize that $\frac{3\pi}{8}$ is half of $\frac{3\pi}{4}$. Thus, we use $\theta = \frac{3\pi}{4}$ in the formula. Since $\cos \frac{3\pi}{4} = -\frac{\sqrt{2}}{2}$, we get $\sin \frac{3\pi}{8} = \sqrt{\frac{1 - (-\frac{\sqrt{2}}{2})}{2}} = \frac{1}{2}\sqrt{2 + \sqrt{2}}$, which matches choice A.

Use the Half-Angle Formulas - sin⁡3π8\sin \frac { 3 \pi } { 8 }sin83π​

Use the Half-Angle Formulas
- $\sin \frac { 3 \pi } { 8 }$