Question

What is the value of $\sin \left(\frac{5 \pi}{12}\right) ?$

• A. $\frac{\sqrt{3}+1}{2}$
• B. $\frac{\sqrt{6}+\sqrt{2}}{4}$
• C. $\frac{\sqrt{3}+\sqrt{2}}{4}$
• D. $\frac{\sqrt{6}+1}{2}$

Answer 1

Answer: (B)

$\sin \frac{5 \pi}{12}=\sin 75^{\circ}$
$=\sin \left(45^{\circ}+30^{\circ}\right)=\sin 45^{\circ} \cos 30^{\circ}+\cos 45^{\circ} \sin 35^{\circ}$
$=\frac{1}{\sqrt{2}} \cdot \frac{\sqrt{3}}{2}+\frac{1}{\sqrt{2}} \cdot \frac{1}{2}=\frac{1}{\sqrt{2}}\left(\frac{\sqrt{3}+1}{2}\right)$
$=\frac{\sqrt{3}+1}{2 \sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{6}+\sqrt{2}}{4}$