Question

Solve the angle using half-angle formula.Sin 5pi/12 half angle

Answer 1

Given:

$sin(\frac{5\pi}{12})$

Let's solve using the half angle formula.

To solve using half-angle formula, take the following steps.

Step 1.

Split the angle into two angles:

$sin(\frac{\pi}{6}+\frac{\pi}{4})$

Step 2.

Apply the sum of angles identity:

$sin(\frac{\pi}{6})cos(\frac{\pi}{4})+cos(\frac{\pi}{6})sin(\frac{\pi}{4})$

Step 3.

Now, use the exact values of each:

$\begin{gathered} \frac{1}{2}*\frac{\sqrt{2}}{2}+\frac{\sqrt{3}}{2}*\frac{\sqrt{2}}{2} \\ \\ \end{gathered}$

Step 4.

Simplify

$\begin{gathered} \frac{1}{2}*\frac{\sqrt{2}}{2}+\frac{\sqrt{3}}{2}*\frac{\sqrt{2}}{2} \\ \\ \frac{\sqrt{2}}{2*2}+\frac{\sqrt{3}*\sqrt{2}}{2*2} \\ \\ \frac{\sqrt{2}}{4}+\frac{\sqrt{6}}{4} \\ \\ =\frac{\sqrt{2}+\sqrt{6}}{4} \end{gathered}$

ANSWER:

$\frac{\sqrt{2}+\sqrt{6}}{4}$